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270.00 scf sf 525 2925 m gs 1 -1 sc (a) col0 sh gr /Times-Roman ff 240.00 scf sf 450 3405 m gs 1 -1 sc (.60) col0 sh gr /Times-Roman ff 240.00 scf sf 1080 3405 m gs 1 -1 sc (.40) col0 sh gr % Polyline n 9285 6945 m 9405 6945 l gs col0 s gr /Times-Bold ff 270.00 scf sf 9315 7215 m gs 1 -1 sc (d) col0 sh gr % Polyline n 8130 7890 m 8250 7890 l gs col0 s gr /Times-Bold ff 270.00 scf sf 8130 8100 m gs 1 -1 sc (c) col0 sh gr % Polyline 15.000 slw n 7890 7320 m 9675 7320 l gs col0 s gr % Polyline n 8490 6840 m 8475 8205 l gs col0 s gr % Polyline 7.500 slw n 7890 6840 m 9675 6840 l 9675 8205 l 7890 8205 l cp gs col0 s gr % Polyline n 9075 6840 m 9075 8205 l gs col0 s gr % Polyline n 7905 7740 m 9675 7740 l gs col0 s gr /Times-Bold ff 270.00 scf sf 8130 7590 m gs 1 -1 sc (c) col0 sh gr /Times-Bold ff 270.00 scf sf 8745 7215 m gs 1 -1 sc (d) col0 sh gr /Times-Roman ff 240.00 scf sf 8640 7605 m gs 1 -1 sc (.50) col0 sh gr /Times-Roman ff 240.00 scf sf 9225 7620 m gs 1 -1 sc (.50) col0 sh gr /Times-Roman ff 240.00 scf sf 8640 8070 m gs 1 -1 sc (.40) col0 sh gr /Times-Roman ff 240.00 scf sf 9225 8070 m gs 1 -1 sc (.60) col0 sh gr % Polyline n 5355 7920 m 5475 7920 l gs col0 s gr /Times-Bold ff 270.00 scf sf 5355 8130 m gs 1 -1 sc (b) col0 sh gr % Polyline n 6510 6975 m 6630 6975 l gs col0 s gr /Times-Bold ff 270.00 scf sf 6540 7245 m gs 1 -1 sc (c) col0 sh gr % Polyline 15.000 slw n 5115 7350 m 6900 7350 l gs col0 s gr % Polyline n 5715 6870 m 5700 8235 l gs col0 s gr % Polyline 7.500 slw n 5115 6870 m 6900 6870 l 6900 8235 l 5115 8235 l cp gs col0 s gr % Polyline n 6300 6870 m 6300 8235 l gs col0 s gr % Polyline n 5130 7770 m 6900 7770 l gs col0 s gr /Times-Bold ff 270.00 scf sf 5355 7620 m gs 1 -1 sc (b) col0 sh gr /Times-Bold ff 270.00 scf sf 5970 7245 m gs 1 -1 sc (c) col0 sh gr /Times-Roman ff 240.00 scf sf 6450 7650 m gs 1 -1 sc (.30) col0 sh gr /Times-Roman ff 240.00 scf sf 5865 8100 m gs 1 -1 sc (.15) col0 sh gr /Times-Roman ff 240.00 scf sf 6450 8100 m gs 1 -1 sc (.85) col0 sh gr /Times-Roman ff 240.00 scf sf 5865 7635 m gs 1 -1 sc (.70) col0 sh gr % Polyline n 3810 6975 m 3930 6975 l gs col0 s gr /Times-Bold ff 270.00 scf sf 3840 7245 m gs 1 -1 sc (b) col0 sh gr % Polyline n 2655 7920 m 2775 7920 l gs col0 s gr /Times-Bold ff 270.00 scf sf 2655 8130 m gs 1 -1 sc (a) col0 sh gr % Polyline 15.000 slw n 2415 7350 m 4200 7350 l gs col0 s gr % Polyline n 3015 6870 m 3000 8235 l gs col0 s gr % Polyline 7.500 slw n 2415 6870 m 4200 6870 l 4200 8235 l 2415 8235 l cp gs col0 s gr % Polyline n 3600 6870 m 3600 8235 l gs col0 s gr % Polyline n 2430 7770 m 4200 7770 l gs col0 s gr /Times-Bold ff 270.00 scf sf 2655 7620 m gs 1 -1 sc (a) col0 sh gr /Times-Bold ff 270.00 scf sf 3270 7245 m gs 1 -1 sc (b) col0 sh gr /Times-Roman ff 240.00 scf sf 3165 7635 m gs 1 -1 sc (.90) col0 sh gr /Times-Roman ff 240.00 scf sf 3750 7650 m gs 1 -1 sc (.10) col0 sh gr /Times-Roman ff 240.00 scf sf 3165 8100 m gs 1 -1 sc (.20) col0 sh gr /Times-Roman ff 240.00 scf sf 3750 8100 m gs 1 -1 sc (.80) col0 sh gr % Polyline n 3810 2775 m 3930 2775 l gs col0 s gr /Times-Bold ff 270.00 scf sf 3840 3045 m gs 1 -1 sc (b) col0 sh gr % Polyline n 2655 3720 m 2775 3720 l gs col0 s gr /Times-Bold ff 270.00 scf sf 2655 3930 m gs 1 -1 sc (a) col0 sh gr % Polyline 15.000 slw n 2415 3150 m 4200 3150 l gs col0 s gr % Polyline n 3015 2670 m 3000 4035 l gs col0 s gr % Polyline 7.500 slw n 2415 2670 m 4200 2670 l 4200 4035 l 2415 4035 l cp gs col0 s gr % Polyline n 3600 2670 m 3600 4035 l gs col0 s gr % Polyline n 2430 3570 m 4200 3570 l gs col0 s gr /Times-Bold ff 270.00 scf sf 2655 3420 m gs 1 -1 sc (a) col0 sh gr /Times-Bold ff 270.00 scf sf 3270 3045 m gs 1 -1 sc (b) col0 sh gr /Times-Roman ff 240.00 scf sf 3165 3435 m gs 1 -1 sc (.90) col0 sh gr /Times-Roman ff 240.00 scf sf 3750 3450 m gs 1 -1 sc (.10) col0 sh gr /Times-Roman ff 240.00 scf sf 3165 3900 m gs 1 -1 sc (.20) col0 sh gr /Times-Roman ff 240.00 scf sf 3750 3900 m gs 1 -1 sc (.80) col0 sh gr % Polyline n 1125 6945 m 1245 6945 l gs col0 s gr /Times-Bold ff 270.00 scf sf 1125 7155 m gs 1 -1 sc (a) col0 sh gr % Polyline 15.000 slw n 885 6870 m 885 7755 l gs col0 s gr % Polyline n 300 7305 m 1515 7305 l gs col0 s gr % Polyline 7.500 slw n 285 6870 m 1515 6870 l 1515 7755 l 285 7755 l cp gs col0 s gr /Times-Bold ff 270.00 scf sf 510 7155 m gs 1 -1 sc (a) col0 sh gr /Times-Roman ff 240.00 scf sf 435 7635 m gs 1 -1 sc (.60) col0 sh gr /Times-Roman ff 240.00 scf sf 1065 7635 m gs 1 -1 sc (.40) col0 sh gr % Polyline n 10815 2595 m 10935 2595 l gs col0 s gr /Times-Bold ff 270.00 scf sf 10815 2865 m gs 1 -1 sc (d) col0 sh gr % Polyline n 10815 6780 m 10935 6780 l gs col0 s gr /Times-Bold ff 270.00 scf sf 10815 7050 m gs 1 -1 sc (d) col0 sh gr % Polyline 15.000 slw n 2820 4575 m 2970 4575 l gs col0 s gr /Times-Bold ff 270.00 scf sf 2850 4815 m gs 1 -1 sc (b) col0 sh gr % Ellipse n 11146 1070 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 9324 2027 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 6567 2005 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 3857 2005 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 1123 2005 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 11131 5255 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 9309 6212 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 6552 6190 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 3842 6190 410 410 0 360 DrawEllipse gs col0 s gr % Ellipse n 1108 6190 410 410 0 360 DrawEllipse gs col0 s gr % Polyline gs clippath 3106 1967 m 3346 2027 l 3106 2087 l 3430 2087 l 3430 1967 l cp clip n 1533 2027 m 3400 2027 l gs col0 s gr gr % arrowhead n 3106 1967 m 3346 2027 l 3106 2087 l col0 s % Polyline gs clippath 5840 1967 m 6080 2027 l 5840 2087 l 6164 2087 l 6164 1967 l cp clip n 4290 2027 m 6134 2027 l gs col0 s gr gr % arrowhead n 5840 1967 m 6080 2027 l 5840 2087 l col0 s % Polyline gs clippath 8620 1945 m 8860 2005 l 8620 2065 l 8944 2065 l 8944 1945 l cp clip n 7000 2005 m 8914 2005 l gs col0 s gr gr % arrowhead n 8620 1945 m 8860 2005 l 8620 2065 l col0 s % Polyline gs clippath 10545 1442 m 10781 1370 l 10606 1545 l 10885 1379 l 10823 1276 l cp clip n 9757 1983 m 10828 1343 l gs col0 s gr gr % arrowhead n 10545 1442 m 10781 1370 l 10606 1545 l col0 s % Polyline gs clippath 3091 6152 m 3331 6212 l 3091 6272 l 3415 6272 l 3415 6152 l cp clip n 1518 6212 m 3385 6212 l gs col0 s gr gr % arrowhead n 3091 6152 m 3331 6212 l 3091 6272 l col0 s % Polyline gs clippath 5825 6152 m 6065 6212 l 5825 6272 l 6149 6272 l 6149 6152 l cp clip n 4275 6212 m 6119 6212 l gs col0 s gr gr % arrowhead n 5825 6152 m 6065 6212 l 5825 6272 l col0 s % Polyline gs clippath 8605 6130 m 8845 6190 l 8605 6250 l 8929 6250 l 8929 6130 l cp clip n 6985 6190 m 8899 6190 l gs col0 s gr gr % arrowhead n 8605 6130 m 8845 6190 l 8605 6250 l col0 s % Polyline gs clippath 10530 5627 m 10766 5555 l 10591 5730 l 10870 5564 l 10808 5461 l cp clip n 9742 6168 m 10813 5528 l gs col0 s gr gr % arrowhead n 10530 5627 m 10766 5555 l 10591 5730 l col0 s % Polyline 7.500 slw gs clippath 10648 843 m 10745 919 l 10623 898 l 10772 964 l 10796 909 l cp clip n 10500 810 m 10770 930 l gs col1 s gr gr % arrowhead n 10648 843 m 10745 919 l 10623 898 l col1 s % Polyline gs clippath 10573 4993 m 10670 5069 l 10548 5048 l 10697 5114 l 10721 5059 l cp clip n 10425 4960 m 10695 5080 l gs col1 s gr gr % arrowhead n 10573 4993 m 10670 5069 l 10548 5048 l col1 s % Polyline n 270 4500 m 12570 4500 l gs col0 s gr % Polyline n 300 300 m 12600 300 l gs col0 s gr % Polyline 15.000 slw n 825 4590 m 975 4590 l gs col0 s gr % Polyline 7.500 slw n 285 8700 m 12585 8700 l gs col0 s gr % Polyline n 4200 1725 m 4575 1425 l gs col1 s gr % Polyline n 4207 5934 m 4582 5634 l gs col1 s gr % Polyline 15.000 slw n 3195 2745 m 3450 2745 l 3450 3105 l 3195 3105 l cp gs col0 s gr % Polyline n 3750 6915 m 4005 6915 l 4005 7290 l 3750 7290 l cp gs col0 s gr % Polyline n 11220 1620 m 11205 3015 l gs col0 s gr % Polyline n 10635 2040 m 12450 2025 l gs col0 s gr % Polyline 7.500 slw n 10635 2505 m 12435 2505 l gs col0 s gr % Polyline n 12060 1695 m 12180 1695 l gs col0 s gr % Polyline n 10620 1620 m 12450 1620 l 12450 3015 l 10620 3015 l cp gs col0 s gr % Polyline n 11820 1620 m 11820 3015 l gs col0 s gr % Polyline 15.000 slw n 11205 5805 m 11190 7200 l gs col0 s gr % Polyline n 10620 6225 m 12435 6210 l gs col0 s gr % Polyline 7.500 slw n 10620 6690 m 12420 6690 l gs col0 s gr % Polyline n 11805 5805 m 11805 7215 l gs col0 s gr % Polyline n 12045 5880 m 12165 5880 l gs col0 s gr % Polyline n 10605 5805 m 12435 5805 l 12435 7200 l 10605 7200 l cp gs col0 s gr /Times-Bold ff 420.00 scf sf 986 2141 m gs 1 -1 sc (A) col0 sh gr /Times-Bold ff 420.00 scf sf 3720 2164 m gs 1 -1 sc (B) col0 sh gr /Times-Bold ff 420.00 scf sf 6408 2164 m gs 1 -1 sc (C) col0 sh gr /Times-Bold ff 420.00 scf sf 9188 2186 m gs 1 -1 sc (D) col0 sh gr /Times-Bold ff 420.00 scf sf 11010 1229 m gs 1 -1 sc (E) col0 sh gr /Times-Bold ff 420.00 scf sf 971 6326 m gs 1 -1 sc (A) col0 sh gr /Times-Bold ff 420.00 scf sf 3705 6349 m gs 1 -1 sc (B) col0 sh gr /Times-Bold ff 420.00 scf sf 6393 6349 m gs 1 -1 sc (C) col0 sh gr /Times-Bold ff 420.00 scf sf 9173 6371 m gs 1 -1 sc (D) col0 sh gr /Times-Bold ff 420.00 scf sf 10995 5414 m gs 1 -1 sc (E) col0 sh gr /Times-Bold ff 270.00 scf sf 11475 1920 m gs 1 -1 sc (e) col0 sh gr /Times-Bold ff 270.00 scf sf 12060 1905 m gs 1 -1 sc (e) col0 sh gr /Times-Roman ff 240.00 scf sf 11370 2370 m gs 1 -1 sc (.25) col0 sh gr /Times-Roman ff 240.00 scf sf 11970 2370 m gs 1 -1 sc (.75) col0 sh gr /Times-Roman ff 240.00 scf sf 11970 2820 m gs 1 -1 sc (.75) col0 sh gr /Times-Roman ff 240.00 scf sf 11370 2820 m gs 1 -1 sc (.25) col0 sh gr /Times-Bold ff 270.00 scf sf 10845 2385 m gs 1 -1 sc (d) col0 sh gr /Times-Bold ff 270.00 scf sf 11460 6105 m gs 1 -1 sc (e) col0 sh gr /Times-Bold ff 270.00 scf sf 12045 6090 m gs 1 -1 sc (e) col0 sh gr /Times-Bold ff 270.00 scf sf 10830 6570 m gs 1 -1 sc (d) col0 sh gr /Times-Roman ff 240.00 scf sf 11340 6540 m gs 1 -1 sc (.90) col0 sh gr /Times-Roman ff 240.00 scf sf 11955 6540 m gs 1 -1 sc (.10) col0 sh gr /Times-Roman ff 240.00 scf sf 11340 7005 m gs 1 -1 sc (.05) col0 sh gr /Times-Roman ff 240.00 scf sf 11955 6990 m gs 1 -1 sc (.95) col0 sh gr /Times-Bold ff 270.00 scf sf 270 615 m gs 1 -1 sc (Case b: Network ) col0 sh gr /Times-Bold ff 270.00 scf sf 2850 600 m gs 1 -1 sc (b) col0 sh gr /Times-Bold ff 270.00 scf sf 255 4815 m gs 1 -1 sc (Case b: Network ) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 604 1806 a FE(Figure)27 b(2:)36 b(Instan)n(tiating)27 b(v)-5 b(ariables)26 b(to)i(render)f(the)h(net)n(w)n(ork)e (singly{connected.)125 2071 y(Note)39 b(that)h(net)n(w)n(ork)f Fw(<)9 b Fv(N)j Fw(;)i(b)9 b(>)39 b FE(of)h(Figure)f(2)g(w)n(as)g (obtained)h(using)f(a)g Fx(lo)l(c)l(al)j(tr)l(ansformation)f FE(to)f(net)n(w)n(ork)e Fv(N)52 b FE(of)0 2171 y(Figure)27 b(1:)101 2337 y(1.)42 b(w)n(e)27 b(deleted)h(the)g(edge)f Fw(B)t Fv(!)p Fw(E)5 b FE(;)1187 2306 y Fq(2)101 2503 y FE(2.)42 b(w)n(e)27 b(reduced)g(the)h(conditional)f(probabilit)n(y)g (table)g(\(CPT\))h(of)f(no)r(de)h Fw(E)33 b FE(from)p 1271 2635 590 4 v 1269 2734 4 100 v 1448 2734 V 1500 2704 a Fw(e)p 1654 2734 V 1705 2659 39 4 v 166 w(e)p 1860 2734 4 100 v 1271 2738 590 4 v 1269 2837 4 100 v 1321 2807 a(bd)p 1448 2837 V 100 w(:)p FE(25)p 1654 2837 V 98 w Fw(:)p FE(75)p 1860 2837 V 1271 2840 590 4 v 1269 2945 4 105 v 1321 2915 a Fw(b)p 1357 2847 44 4 v(d)p 1448 2945 4 105 v 100 w(:)p FE(25)p 1654 2945 V 98 w Fw(:)p FE(75)p 1860 2945 V 1271 2948 590 4 v 1269 3052 4 105 v 1321 2955 36 4 v 1321 3022 a Fw(bd)p 1448 3052 4 105 v 100 w(:)p FE(90)p 1654 3052 V 98 w Fw(:)p FE(10)p 1860 3052 V 1271 3055 590 4 v 1269 3160 4 105 v 1321 3062 36 4 v 1321 3130 a Fw(b)p 1357 3062 44 4 v(d)p 1448 3160 4 105 v 100 w(:)p FE(05)p 1654 3160 V 98 w Fw(:)p FE(95)p 1860 3160 V 1271 3163 590 4 v 2035 2918 a(to)p 2282 2742 555 4 v 2280 2842 4 100 v 2423 2842 V 2475 2812 a Fw(e)p 2629 2842 V 2680 2766 39 4 v 166 w(e)p 2835 2842 4 100 v 2282 2845 555 4 v 2280 2945 4 100 v 2332 2915 a(d)p 2423 2945 V 100 w(:)p FE(25)p 2629 2945 V 98 w Fw(:)p FE(75)p 2835 2945 V 2282 2948 555 4 v 2280 3052 4 105 v 2332 2955 44 4 v 2332 3022 a Fw(d)p 2423 3052 4 105 v 100 w(:)p FE(25)p 2629 3052 V 98 w Fw(:)p FE(75)p 2835 3052 V 2282 3055 555 4 v 208 3328 a(in)27 b(order)g(to)g(re\015ect)g(the)h(assumption)g(that)f Fw(B)32 b FE(is)c(instan)n(tiated)f(to)h Fw(b)p FE(.)101 3495 y(3.)42 b(w)n(e)27 b(recorded)f(the)i(observ)-5 b(ation)26 b Fw(b)h FE(\(sho)n(wn)h(pictorially)e(b)n(y)h(a)h(b)r(o)n (x)f(around)f(the)i(v)-5 b(alue)28 b Fw(b)f FE(in)h(the)g(CPT)f(for)g Fw(B)t FE(\).)0 3661 y(Note)i(that)h(the)f(result)g(of)g(the)h(ab)r(o)n (v)n(e)d Fx(instantiation)32 b(op)l(er)l(ation)e FE(is)f(not)g(simply)h (a)e(Ba)n(y)n(esian)f(net)n(w)n(ork,)i(but)g(a)g(Ba)n(y)n(esian)0 3760 y(net)n(w)n(ork)d(together)h(with)h(some)f(asso)r(ciated)f (evidence.)125 3860 y(In)33 b(general,)g(w)n(e)g(will)g(use)g(the)h (term)f 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810 4170 m gs 1 -1 sc (1) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 1485 4500 m gs 1 -1 sc (2) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 2055 4770 m gs 1 -1 sc (3) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 2670 5100 m gs 1 -1 sc (4) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 3285 5385 m gs 1 -1 sc (5) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 3855 5685 m gs 1 -1 sc (6) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 4530 6000 m gs 1 -1 sc (7) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 11280 5415 m gs 1 -1 sc (4) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 1620 7215 m gs 1 -1 sc (a\) Cutsets) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 6165 7215 m gs 1 -1 sc (b\) A-Cutsets) col0 sh gr /Times-Italic-iso ff 210.00 scf sf 10485 7215 m gs 1 -1 sc (c\) Contexts) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 956 1442 a FE(Figure)27 b(10:)36 b(Cutsets,)28 b(a{cutsets)f(and)g(con)n(texts)g(of)h(a)f(dtree.)0 1707 y(random)g(net)n(w)n(orks.)36 b(F)-7 b(or)27 b(the)h(\014rst)g(set)g (of)g(net)n(w)n(orks,)e Ff(Set-A)p FE(,)i(whic)n(h)g(con)n(tain)f (100-no)r(de)f(net)n(w)n(orks)g(with)i(elimination-)0 1807 y(order)c(width)i Fv(\024)d FE(20,)i(the)h(a-cutset)f(width)h (divided)g(b)n(y)f(elimination-order)f(width)i(w)n(as)f(3)p Fw(:)p FE(5)f(on)i(a)n(v)n(erage.)33 b(F)-7 b(or)25 b(the)h(second)0 1906 y(set)31 b(of)g(net)n(w)n(orks,)f Ff(Set-B)p FE(,)i(whic)n(h)f (con)n(tain)f(150-no)r(de)f(net)n(w)n(orks)g(with)j(elimination-order)d (width)i Fv(\024)e FE(50,)i(this)g(a)n(v)n(erage)0 2006 y(w)n(as)21 b(2)p Fw(:)p FE(4.)34 b(This)22 b(giv)n(es)f(an)h(idea)g (of)g(what)g(the)h(constan)n(t)e(factors)g(in)h(exp\()p Fw(w)17 b FE(log)d Fw(n)p FE(\))22 b(are)g(for)f(this)i(class)e(of)h (net)n(w)n(orks.)33 b(Second,)0 2106 y(the)28 b Fw(O)r FE(\()p Fw(n)14 b FE(exp\()p Fw(w)j FE(log)d Fw(n)p FE(\)\))28 b(time)g(complexit)n(y)f(is)h(not)g(comparable)e(to)h(that)h(of)f (cutset)h(conditioning.)37 b(Ho)n(w)n(ev)n(er:)125 2272 y Fv(\017)k FE(When)33 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b(in)n(ten)n(tion)f(here)g(is)h(for)f Fu(cf)6 b FE(\()p Fw(T)12 b FE(\))31 b(to)h(b)r(e)g(the)g(fraction)e(of)i Fu(cache)2128 3827 y Fj(T)2212 3815 y FE(whic)n(h)g(will)g(b)r(e)g (\014lled)g(b)n(y)f(algorithm)f Ff(r)n(c)q FE(.)49 b(That)31 b(is,)0 3915 y(if)g Fu(cf)6 b FE(\()p Fw(T)12 b FE(\))27 b(=)g Fw(:)p FE(2,)j(then)h(w)n(e)e(will)i(only)f(use)g(20\045)f(of)h (the)h(total)f(storage)e(required)h(b)n(y)h Fu(cache)2870 3927 y Fj(T)2923 3915 y FE(.)44 b(Note)30 b(that)h(algorithm)e Ff(r)n(c1)0 4014 y FE(corresp)r(onds)j(to)i(the)h(case)e(where)h Fu(cf)6 b FE(\()p Fw(T)12 b FE(\))33 b(=)h(0)g(for)f(ev)n(ery)g(no)r (de)h Fw(T)12 b FE(.)56 b(Moreo)n(v)n(er,)33 b(algorithm)g Ff(r)n(c2)h FE(corresp)r(onds)f(to)h(the)0 4114 y(case)28 b(where)f Fu(cf)6 b FE(\()p Fw(T)12 b FE(\))24 b(=)g(1.)39 b(F)-7 b(or)28 b(eac)n(h)f(of)i(these)f(cases,)g(w)n(e)g(pro)n(vided)f (a)h(coun)n(t)g(of)g(the)h(recursiv)n(e)e(calls)h(made)g(b)n(y)g (recursiv)n(e)0 4214 y(conditioning.)36 b(The)26 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b(that)f(w)n(e)g(can)0 4811 y(enforce)20 b(the)h(assumption)f (that)g(an)n(y)g(giv)n(en)g(instan)n(tiation)g Ft(y)i FE(of)e Fu(context)p FE(\()p Fw(T)12 b FE(\))20 b(is)g(equally)g(lik)n (ely)g(to)g(b)r(e)h(cac)n(hed)f(b)n(y)g(randomly)0 4911 y(c)n(ho)r(osing)26 b(the)i(instan)n(tiations)f(to)g(b)r(e)h(cac)n (hed.)0 5079 y Ft(Theorem)i(6)42 b Fx(If)31 b(the)g(size)g(of)g Fu(cache)1176 5091 y Fj(T)1259 5079 y Fx(is)g(limite)l(d)g(to)g Fu(cf)6 b FE(\()p Fw(T)12 b FE(\))30 b Fx(of)h(its)g(ful)t(l)g(size,)h (and)f(if)h(e)l(ach)f(instantiation)g(of)h Fu(context)o FE(\()p Fw(T)12 b FE(\))0 5179 y Fx(is)35 b(e)l(qual)t(ly)g(likely)h (to)e(b)l(e)g(c)l(ache)l(d)h(on)g(line)f(10)h(of)g Ff(r)n(c)q Fx(,)g(the)g(aver)l(age)g(numb)l(er)f(of)h(c)l(al)t(ls)g(made)g(to)f(a) h(non{r)l(o)l(ot)f(no)l(de)h Fw(T)45 b Fx(in)0 5278 y(algorithm)31 b Ff(r)n(c)f Fx(is)736 5378 y Fu(ave)p FE(\()p Fw(T)12 b FE(\))23 b(=)g Fu(cutset)o FE(\()p Fw(T)1388 5344 y Fj(p)1426 5378 y FE(\))1458 5344 y Fq(#)1531 5311 y Fs(\002)1565 5378 y Fu(cf)6 b FE(\()p Fw(T)1726 5344 y Fj(p)1764 5378 y FE(\))p Fu(context)p FE(\()p Fw(T)2146 5344 y Fj(p)2183 5378 y FE(\))2215 5344 y Fq(#)2293 5378 y FE(+)18 b(\(1)g Fv(\000)g Fu(cf)6 b FE(\()p Fw(T)2712 5344 y Fj(p)2750 5378 y FE(\)\))p Fu(ave)p FE(\()p Fw(T)3022 5344 y Fj(p)3060 5378 y FE(\))3092 5311 y Fs(\003)3141 5378 y Fw(:)1908 5656 y FE(12)p eop %%Page: 13 13 13 12 bop 651 1909 a @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 3118 @rwi @setspecial %%BeginDocument: est.ps %!PS-Adobe-2.0 EPSF-2.0 %%Title: c:/windows/desktop/rc/results/n10020/est.ps %%Creator: gnuplot 3.7 patchlevel 0 %%CreationDate: Tue Jul 13 10:32:19 1999 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -53 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Latex) findfont 160 scalefont setfont 1.000 UL LTb 720 480 M 63 0 V 6145 0 R -63 0 V 624 480 M (0.2) Rshow 720 990 M 63 0 V 6145 0 R -63 0 V 624 990 M (0.4) Rshow 720 1500 M 63 0 V 6145 0 R -63 0 V -6241 0 R (0.6) Rshow 720 2010 M 63 0 V 6145 0 R -63 0 V -6241 0 R (0.8) Rshow 720 2520 M 63 0 V 6145 0 R -63 0 V -6241 0 R (1) Rshow 720 3030 M 63 0 V 6145 0 R -63 0 V -6241 0 R (1.2) Rshow 720 3540 M 63 0 V 6145 0 R -63 0 V -6241 0 R (1.4) Rshow 720 4050 M 63 0 V 6145 0 R -63 0 V -6241 0 R (1.6) Rshow 720 4560 M 63 0 V 6145 0 R -63 0 V -6241 0 R (1.8) Rshow 720 480 M 0 63 V 0 4017 R 0 -63 V 720 320 M (0) Cshow 1341 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (100) Cshow 1962 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (200) Cshow 2582 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (300) Cshow 3203 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (400) Cshow 3824 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (500) Cshow 4445 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (600) Cshow 5066 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (700) Cshow 5686 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (800) Cshow 6307 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (900) Cshow 6928 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (1000) Cshow 1.000 UL LTb 720 480 M 6208 0 V 0 4080 V -6208 0 V 720 480 L 160 2520 M currentpoint gsave translate 90 rotate 0 0 M (Measured No. Calls / Estimated No. Calls) Cshow grestore 3824 80 M (Samples) Cshow 3824 4800 M (Estimating the Running Time of RC under Variable Space) Cshow 1.000 UP 1.000 UL LT0 720 2520 Pls 726 2336 Pls 732 2592 Pls 739 2523 Pls 745 2864 Pls 751 2499 Pls 757 2593 Pls 763 2497 Pls 770 2907 Pls 776 2964 Pls 782 2520 Pls 788 2520 Pls 794 2612 Pls 801 2464 Pls 807 2523 Pls 813 2631 Pls 819 2729 Pls 826 2583 Pls 832 2501 Pls 838 2520 Pls 844 2679 Pls 850 2469 Pls 857 2517 Pls 863 2520 Pls 869 2520 Pls 875 2578 Pls 881 2543 Pls 888 2520 Pls 894 2552 Pls 900 2526 Pls 906 2701 Pls 912 2538 Pls 919 2282 Pls 925 2768 Pls 931 2543 Pls 937 2524 Pls 943 2520 Pls 950 2521 Pls 956 2520 Pls 962 2365 Pls 968 2534 Pls 975 2520 Pls 981 2525 Pls 987 2520 Pls 993 2584 Pls 999 2623 Pls 1006 2451 Pls 1012 2520 Pls 1018 2530 Pls 1024 2520 Pls 1030 2599 Pls 1037 2578 Pls 1043 2544 Pls 1049 2532 Pls 1055 2549 Pls 1061 2589 Pls 1068 2611 Pls 1074 2521 Pls 1080 2608 Pls 1086 2666 Pls 1092 2994 Pls 1099 2530 Pls 1105 2588 Pls 1111 2562 Pls 1117 2574 Pls 1124 2701 Pls 1130 2843 Pls 1136 2520 Pls 1142 2612 Pls 1148 2518 Pls 1155 2519 Pls 1161 2591 Pls 1167 2504 Pls 1173 2937 Pls 1179 2556 Pls 1186 3175 Pls 1192 2520 Pls 1198 2520 Pls 1204 2520 Pls 1210 2520 Pls 1217 2506 Pls 1223 2520 Pls 1229 2520 Pls 1235 2504 Pls 1241 2544 Pls 1248 2608 Pls 1254 2533 Pls 1260 2517 Pls 1266 2520 Pls 1273 2522 Pls 1279 2556 Pls 1285 2651 Pls 1291 2763 Pls 1297 2538 Pls 1304 2512 Pls 1310 2544 Pls 1316 2594 Pls 1322 2519 Pls 1328 2520 Pls 1335 2503 Pls 1341 2552 Pls 1347 2481 Pls 1353 2522 Pls 1359 2469 Pls 1366 2520 Pls 1372 2365 Pls 1378 2652 Pls 1384 2520 Pls 1390 2625 Pls 1397 2539 Pls 1403 2919 Pls 1409 2566 Pls 1415 2566 Pls 1422 2520 Pls 1428 2703 Pls 1434 2613 Pls 1440 2585 Pls 1446 2595 Pls 1453 2520 Pls 1459 2789 Pls 1465 2830 Pls 1471 2533 Pls 1477 2520 Pls 1484 2533 Pls 1490 2521 Pls 1496 2785 Pls 1502 2572 Pls 1508 2722 Pls 1515 2520 Pls 1521 2564 Pls 1527 2741 Pls 1533 2526 Pls 1539 2520 Pls 1546 2531 Pls 1552 2943 Pls 1558 2520 Pls 1564 2548 Pls 1570 2694 Pls 1577 2520 Pls 1583 2520 Pls 1589 2556 Pls 1595 2520 Pls 1602 2525 Pls 1608 2443 Pls 1614 2519 Pls 1620 2520 Pls 1626 2520 Pls 1633 2510 Pls 1639 2510 Pls 1645 2534 Pls 1651 2573 Pls 1657 2585 Pls 1664 2520 Pls 1670 2551 Pls 1676 2533 Pls 1682 2581 Pls 1688 2630 Pls 1695 2520 Pls 1701 2743 Pls 1707 2675 Pls 1713 2487 Pls 1719 2670 Pls 1726 2520 Pls 1732 2520 Pls 1738 2520 Pls 1744 2911 Pls 1751 2483 Pls 1757 2986 Pls 1763 2528 Pls 1769 2663 Pls 1775 2336 Pls 1782 2538 Pls 1788 2520 Pls 1794 2518 Pls 1800 2520 Pls 1806 2520 Pls 1813 2509 Pls 1819 2301 Pls 1825 2537 Pls 1831 2520 Pls 1837 2611 Pls 1844 2096 Pls 1850 2520 Pls 1856 2944 Pls 1862 2619 Pls 1868 2587 Pls 1875 2114 Pls 1881 2541 Pls 1887 2627 Pls 1893 2740 Pls 1900 2498 Pls 1906 2451 Pls 1912 2551 Pls 1918 2595 Pls 1924 2812 Pls 1931 2556 Pls 1937 2520 Pls 1943 2513 Pls 1949 2520 Pls 1955 2520 Pls 1962 2520 Pls 1968 2534 Pls 1974 2524 Pls 1980 2617 Pls 1986 2520 Pls 1993 2540 Pls 1999 2588 Pls 2005 2565 Pls 2011 2471 Pls 2017 2530 Pls 2024 2526 Pls 2030 2708 Pls 2036 2555 Pls 2042 2584 Pls 2049 2541 Pls 2055 2774 Pls 2061 2699 Pls 2067 2617 Pls 2073 2540 Pls 2080 2616 Pls 2086 2522 Pls 2092 2559 Pls 2098 2520 Pls 2104 2520 Pls 2111 2524 Pls 2117 2520 Pls 2123 2587 Pls 2129 2519 Pls 2135 2540 Pls 2142 2467 Pls 2148 2521 Pls 2154 2643 Pls 2160 2520 Pls 2166 2527 Pls 2173 2551 Pls 2179 2456 Pls 2185 2406 Pls 2191 2520 Pls 2198 2534 Pls 2204 2665 Pls 2210 2611 Pls 2216 2941 Pls 2222 2523 Pls 2229 2595 Pls 2235 2548 Pls 2241 2485 Pls 2247 2520 Pls 2253 2491 Pls 2260 2520 Pls 2266 2532 Pls 2272 2522 Pls 2278 2523 Pls 2284 2858 Pls 2291 2499 Pls 2297 2520 Pls 2303 2579 Pls 2309 2520 Pls 2315 2714 Pls 2322 2590 Pls 2328 2523 Pls 2334 2530 Pls 2340 2550 Pls 2346 2530 Pls 2353 2551 Pls 2359 2581 Pls 2365 2576 Pls 2371 2520 Pls 2378 2520 Pls 2384 2613 Pls 2390 2624 Pls 2396 2602 Pls 2402 2524 Pls 2409 2520 Pls 2415 2518 Pls 2421 2556 Pls 2427 2552 Pls 2433 2698 Pls 2440 2520 Pls 2446 2572 Pls 2452 2784 Pls 2458 2520 Pls 2464 2582 Pls 2471 2409 Pls 2477 2508 Pls 2483 2520 Pls 2489 2879 Pls 2495 2633 Pls 2502 2584 Pls 2508 2522 Pls 2514 2412 Pls 2520 2520 Pls 2527 2544 Pls 2533 2574 Pls 2539 2520 Pls 2545 2739 Pls 2551 2522 Pls 2558 2704 Pls 2564 2520 Pls 2570 2533 Pls 2576 2425 Pls 2582 955 Pls 2589 2534 Pls 2595 2467 Pls 2601 3005 Pls 2607 2524 Pls 2613 2555 Pls 2620 2520 Pls 2626 2520 Pls 2632 2521 Pls 2638 2755 Pls 2644 2520 Pls 2651 2520 Pls 2657 2815 Pls 2663 2536 Pls 2669 2520 Pls 2676 2785 Pls 2682 2516 Pls 2688 2622 Pls 2694 2520 Pls 2700 2575 Pls 2707 2517 Pls 2713 2721 Pls 2719 2520 Pls 2725 2520 Pls 2731 2520 Pls 2738 2540 Pls 2744 2520 Pls 2750 2520 Pls 2756 2565 Pls 2762 2443 Pls 2769 2647 Pls 2775 2595 Pls 2781 2520 Pls 2787 2518 Pls 2793 2631 Pls 2800 2520 Pls 2806 2520 Pls 2812 2825 Pls 2818 2719 Pls 2825 2533 Pls 2831 2565 Pls 2837 2539 Pls 2843 2591 Pls 2849 2381 Pls 2856 2645 Pls 2862 2673 Pls 2868 2367 Pls 2874 2517 Pls 2880 2529 Pls 2887 2516 Pls 2893 2522 Pls 2899 2603 Pls 2905 2558 Pls 2911 2537 Pls 2918 2522 Pls 2924 2710 Pls 2930 2532 Pls 2936 2490 Pls 2942 2570 Pls 2949 2531 Pls 2955 2747 Pls 2961 2318 Pls 2967 2551 Pls 2974 2520 Pls 2980 2640 Pls 2986 2520 Pls 2992 2520 Pls 2998 2604 Pls 3005 2520 Pls 3011 2601 Pls 3017 2520 Pls 3023 2522 Pls 3029 2520 Pls 3036 2526 Pls 3042 2475 Pls 3048 2597 Pls 3054 2544 Pls 3060 2520 Pls 3067 2525 Pls 3073 2586 Pls 3079 2884 Pls 3085 2488 Pls 3091 2521 Pls 3098 2664 Pls 3104 2784 Pls 3110 2645 Pls 3116 2520 Pls 3122 2520 Pls 3129 2458 Pls 3135 2520 Pls 3141 2614 Pls 3147 2542 Pls 3154 2581 Pls 3160 2520 Pls 3166 2470 Pls 3172 2470 Pls 3178 2895 Pls 3185 2530 Pls 3191 2979 Pls 3197 2520 Pls 3203 2524 Pls 3209 2529 Pls 3216 2542 Pls 3222 2540 Pls 3228 2616 Pls 3234 2616 Pls 3240 2613 Pls 3247 2520 Pls 3253 2629 Pls 3259 2520 Pls 3265 2673 Pls 3271 2663 Pls 3278 2612 Pls 3284 2520 Pls 3290 2520 Pls 3296 2654 Pls 3303 2449 Pls 3309 2554 Pls 3315 2507 Pls 3321 2520 Pls 3327 2562 Pls 3334 2497 Pls 3340 2600 Pls 3346 2520 Pls 3352 2520 Pls 3358 2523 Pls 3365 2520 Pls 3371 2569 Pls 3377 2557 Pls 3383 2620 Pls 3389 2520 Pls 3396 2503 Pls 3402 2520 Pls 3408 2520 Pls 3414 2634 Pls 3420 2459 Pls 3427 2521 Pls 3433 2599 Pls 3439 2561 Pls 3445 2512 Pls 3452 2613 Pls 3458 2520 Pls 3464 2520 Pls 3470 2623 Pls 3476 2529 Pls 3483 2638 Pls 3489 2599 Pls 3495 2553 Pls 3501 2491 Pls 3507 2558 Pls 3514 2556 Pls 3520 2526 Pls 3526 2520 Pls 3532 2527 Pls 3538 2560 Pls 3545 2539 Pls 3551 2520 Pls 3557 2537 Pls 3563 2705 Pls 3569 2620 Pls 3576 2515 Pls 3582 2381 Pls 3588 2642 Pls 3594 2501 Pls 3601 2520 Pls 3607 2627 Pls 3613 2771 Pls 3619 2506 Pls 3625 2520 Pls 3632 2714 Pls 3638 2520 Pls 3644 2592 Pls 3650 2968 Pls 3656 2519 Pls 3663 2517 Pls 3669 2520 Pls 3675 2520 Pls 3681 2612 Pls 3687 2742 Pls 3694 2627 Pls 3700 2574 Pls 3706 2570 Pls 3712 2520 Pls 3718 3365 Pls 3725 2731 Pls 3731 2538 Pls 3737 2531 Pls 3743 2529 Pls 3750 2520 Pls 3756 2522 Pls 3762 2379 Pls 3768 2527 Pls 3774 2998 Pls 3781 2561 Pls 3787 2445 Pls 3793 2549 Pls 3799 2520 Pls 3805 2533 Pls 3812 2522 Pls 3818 2520 Pls 3824 2520 Pls 3830 2530 Pls 3836 2636 Pls 3843 2485 Pls 3849 2772 Pls 3855 2523 Pls 3861 2547 Pls 3867 2642 Pls 3874 2522 Pls 3880 2722 Pls 3886 1936 Pls 3892 2907 Pls 3898 2565 Pls 3905 2519 Pls 3911 2520 Pls 3917 2494 Pls 3923 2485 Pls 3930 2520 Pls 3936 2523 Pls 3942 2636 Pls 3948 2660 Pls 3954 2381 Pls 3961 2690 Pls 3967 2562 Pls 3973 2693 Pls 3979 2541 Pls 3985 2614 Pls 3992 2539 Pls 3998 2803 Pls 4004 2543 Pls 4010 2521 Pls 4016 2590 Pls 4023 2520 Pls 4029 2613 Pls 4035 2531 Pls 4041 2520 Pls 4047 2539 Pls 4054 2520 Pls 4060 2557 Pls 4066 3085 Pls 4072 2608 Pls 4079 2699 Pls 4085 2888 Pls 4091 2520 Pls 4097 2520 Pls 4103 2670 Pls 4110 2531 Pls 4116 2521 Pls 4122 2622 Pls 4128 2520 Pls 4134 2750 Pls 4141 2529 Pls 4147 2517 Pls 4153 2592 Pls 4159 2534 Pls 4165 2460 Pls 4172 3448 Pls 4178 2896 Pls 4184 2551 Pls 4190 2520 Pls 4196 2665 Pls 4203 2606 Pls 4209 2706 Pls 4215 2492 Pls 4221 2534 Pls 4228 2514 Pls 4234 2521 Pls 4240 2520 Pls 4246 2520 Pls 4252 2570 Pls 4259 2524 Pls 4265 2621 Pls 4271 2594 Pls 4277 2548 Pls 4283 2520 Pls 4290 2594 Pls 4296 2520 Pls 4302 2706 Pls 4308 2556 Pls 4314 2662 Pls 4321 4098 Pls 4327 2578 Pls 4333 2577 Pls 4339 2540 Pls 4345 2708 Pls 4352 2521 Pls 4358 2535 Pls 4364 2524 Pls 4370 2575 Pls 4377 2541 Pls 4383 2629 Pls 4389 2520 Pls 4395 2521 Pls 4401 3195 Pls 4408 2553 Pls 4414 2893 Pls 4420 2525 Pls 4426 2707 Pls 4432 2520 Pls 4439 1948 Pls 4445 2520 Pls 4451 2795 Pls 4457 2475 Pls 4463 2581 Pls 4470 2523 Pls 4476 2624 Pls 4482 2520 Pls 4488 2612 Pls 4494 2521 Pls 4501 2521 Pls 4507 2529 Pls 4513 2751 Pls 4519 2573 Pls 4526 2444 Pls 4532 2354 Pls 4538 2547 Pls 4544 2571 Pls 4550 2840 Pls 4557 2520 Pls 4563 2509 Pls 4569 2570 Pls 4575 2520 Pls 4581 2959 Pls 4588 2538 Pls 4594 2520 Pls 4600 2553 Pls 4606 2693 Pls 4612 2514 Pls 4619 2507 Pls 4625 2520 Pls 4631 2851 Pls 4637 2556 Pls 4643 2526 Pls 4650 2539 Pls 4656 2571 Pls 4662 2521 Pls 4668 2689 Pls 4674 2815 Pls 4681 2520 Pls 4687 2288 Pls 4693 2541 Pls 4699 2534 Pls 4706 2803 Pls 4712 2517 Pls 4718 2446 Pls 4724 2381 Pls 4730 2640 Pls 4737 2628 Pls 4743 2447 Pls 4749 2564 Pls 4755 2589 Pls 4761 2585 Pls 4768 2631 Pls 4774 2520 Pls 4780 2536 Pls 4786 2567 Pls 4792 2522 Pls 4799 2520 Pls 4805 2563 Pls 4811 2520 Pls 4817 2559 Pls 4823 2520 Pls 4830 2500 Pls 4836 2692 Pls 4842 2569 Pls 4848 2520 Pls 4855 2554 Pls 4861 2617 Pls 4867 2715 Pls 4873 2535 Pls 4879 2670 Pls 4886 2568 Pls 4892 2480 Pls 4898 2619 Pls 4904 2543 Pls 4910 2518 Pls 4917 2520 Pls 4923 2520 Pls 4929 2507 Pls 4935 2595 Pls 4941 2520 Pls 4948 2520 Pls 4954 2520 Pls 4960 2521 Pls 4966 2520 Pls 4972 2685 Pls 4979 2473 Pls 4985 2533 Pls 4991 2520 Pls 4997 2496 Pls 5004 2520 Pls 5010 2547 Pls 5016 2456 Pls 5022 2551 Pls 5028 2699 Pls 5035 3047 Pls 5041 2522 Pls 5047 2530 Pls 5053 2520 Pls 5059 2536 Pls 5066 2676 Pls 5072 2543 Pls 5078 2520 Pls 5084 2656 Pls 5090 2607 Pls 5097 2567 Pls 5103 2660 Pls 5109 2884 Pls 5115 2635 Pls 5121 2452 Pls 5128 2520 Pls 5134 2520 Pls 5140 2583 Pls 5146 2363 Pls 5153 2522 Pls 5159 2523 Pls 5165 2522 Pls 5171 2593 Pls 5177 2487 Pls 5184 2536 Pls 5190 2950 Pls 5196 2763 Pls 5202 2537 Pls 5208 2551 Pls 5215 2525 Pls 5221 2821 Pls 5227 2566 Pls 5233 2678 Pls 5239 2649 Pls 5246 2523 Pls 5252 2713 Pls 5258 2594 Pls 5264 2669 Pls 5270 2577 Pls 5277 2520 Pls 5283 2522 Pls 5289 2520 Pls 5295 2561 Pls 5302 2520 Pls 5308 2501 Pls 5314 2520 Pls 5320 2524 Pls 5326 2633 Pls 5333 2520 Pls 5339 2428 Pls 5345 2841 Pls 5351 2839 Pls 5357 2525 Pls 5364 2555 Pls 5370 2520 Pls 5376 2688 Pls 5382 2533 Pls 5388 2526 Pls 5395 2476 Pls 5401 2541 Pls 5407 2545 Pls 5413 2524 Pls 5419 2465 Pls 5426 2520 Pls 5432 2514 Pls 5438 2643 Pls 5444 2538 Pls 5450 2525 Pls 5457 2519 Pls 5463 2520 Pls 5469 2666 Pls 5475 2511 Pls 5482 2771 Pls 5488 2521 Pls 5494 2885 Pls 5500 2520 Pls 5506 2608 Pls 5513 2667 Pls 5519 2530 Pls 5525 2520 Pls 5531 2564 Pls 5537 2703 Pls 5544 2520 Pls 5550 2578 Pls 5556 2555 Pls 5562 2501 Pls 5568 2536 Pls 5575 2530 Pls 5581 2520 Pls 5587 2586 Pls 5593 2520 Pls 5599 2636 Pls 5606 2527 Pls 5612 2520 Pls 5618 2658 Pls 5624 2565 Pls 5631 2417 Pls 5637 2520 Pls 5643 2531 Pls 5649 2570 Pls 5655 2605 Pls 5662 2953 Pls 5668 2549 Pls 5674 2611 Pls 5680 2740 Pls 5686 2520 Pls 5693 2582 Pls 5699 2884 Pls 5705 2586 Pls 5711 2546 Pls 5717 2625 Pls 5724 2504 Pls 5730 2528 Pls 5736 2570 Pls 5742 2573 Pls 5748 2520 Pls 5755 2520 Pls 5761 2623 Pls 5767 2559 Pls 5773 2520 Pls 5780 2662 Pls 5786 2520 Pls 5792 2520 Pls 5798 3061 Pls 5804 2717 Pls 5811 2520 Pls 5817 2521 Pls 5823 2521 Pls 5829 2524 Pls 5835 2710 Pls 5842 2817 Pls 5848 2418 Pls 5854 2602 Pls 5860 2533 Pls 5866 2523 Pls 5873 2776 Pls 5879 2883 Pls 5885 2520 Pls 5891 2593 Pls 5897 2520 Pls 5904 2496 Pls 5910 2561 Pls 5916 2598 Pls 5922 2529 Pls 5929 2727 Pls 5935 2866 Pls 5941 2520 Pls 5947 2588 Pls 5953 2560 Pls 5960 2496 Pls 5966 2571 Pls 5972 2520 Pls 5978 2366 Pls 5984 2476 Pls 5991 2582 Pls 5997 2532 Pls 6003 2521 Pls 6009 2520 Pls 6015 2637 Pls 6022 2520 Pls 6028 2544 Pls 6034 2466 Pls 6040 2520 Pls 6046 2591 Pls 6053 2619 Pls 6059 3031 Pls 6065 2445 Pls 6071 2520 Pls 6078 2524 Pls 6084 2510 Pls 6090 2737 Pls 6096 2657 Pls 6102 2494 Pls 6109 2734 Pls 6115 2491 Pls 6121 2548 Pls 6127 2487 Pls 6133 2523 Pls 6140 2520 Pls 6146 2529 Pls 6152 2598 Pls 6158 2520 Pls 6164 2527 Pls 6171 2602 Pls 6177 2628 Pls 6183 2448 Pls 6189 2594 Pls 6195 2816 Pls 6202 2587 Pls 6208 2569 Pls 6214 2505 Pls 6220 2618 Pls 6226 2612 Pls 6233 2525 Pls 6239 2524 Pls 6245 2637 Pls 6251 2520 Pls 6258 2543 Pls 6264 2890 Pls 6270 2521 Pls 6276 2520 Pls 6282 2466 Pls 6289 2561 Pls 6295 2587 Pls 6301 2518 Pls 6307 2530 Pls 6313 2560 Pls 6320 2520 Pls 6326 2583 Pls 6332 2593 Pls 6338 2520 Pls 6344 2736 Pls 6351 2555 Pls 6357 2520 Pls 6363 2501 Pls 6369 2550 Pls 6375 2611 Pls 6382 2387 Pls 6388 2521 Pls 6394 2664 Pls 6400 2540 Pls 6407 2520 Pls 6413 2520 Pls 6419 2524 Pls 6425 2690 Pls 6431 2640 Pls 6438 2579 Pls 6444 2907 Pls 6450 2551 Pls 6456 2533 Pls 6462 2525 Pls 6469 2540 Pls 6475 2811 Pls 6481 2524 Pls 6487 2528 Pls 6493 2520 Pls 6500 2517 Pls 6506 2520 Pls 6512 2543 Pls 6518 2602 Pls 6524 2520 Pls 6531 2555 Pls 6537 2520 Pls 6543 2394 Pls 6549 2525 Pls 6556 2520 Pls 6562 2474 Pls 6568 2520 Pls 6574 2530 Pls 6580 2536 Pls 6587 2523 Pls 6593 2393 Pls 6599 2647 Pls 6605 2517 Pls 6611 2520 Pls 6618 2674 Pls 6624 2517 Pls 6630 2522 Pls 6636 2520 Pls 6642 3295 Pls 6649 2522 Pls 6655 2520 Pls 6661 2571 Pls 6667 2520 Pls 6673 2694 Pls 6680 2536 Pls 6686 2680 Pls 6692 2520 Pls 6698 3484 Pls 6705 2648 Pls 6711 2494 Pls 6717 2521 Pls 6723 2577 Pls 6729 2538 Pls 6736 2528 Pls 6742 2576 Pls 6748 3259 Pls 6754 2520 Pls 6760 2533 Pls 6767 2520 Pls 6773 2520 Pls 6779 3277 Pls 6785 2349 Pls 6791 2520 Pls 6798 2520 Pls 6804 2605 Pls 6810 2520 Pls 6816 2428 Pls 6822 2568 Pls 6829 2531 Pls 6835 2594 Pls 6841 2520 Pls 6847 2528 Pls 6854 2518 Pls 6860 2514 Pls 6866 2533 Pls 6872 2548 Pls 6878 2520 Pls 6885 2577 Pls 6891 2533 Pls 6897 2839 Pls 6903 2569 Pls 6909 2363 Pls 6916 2643 Pls 6922 2520 Pls stroke grestore end showpage %%Trailer %%DocumentFonts: Latex %%EndDocument @endspecial 0 2175 a FE(Figure)26 b(13:)35 b(The)27 b(a)n(v)n(erage)c(ratio)j(of)g(measured)g(o)n(v)n(er)e(estimated)j(n)n (um)n(b)r(er)f(of)h(calls)e(is)i(1)p Fw(:)p FE(02)e(and)h(the)h (standard)f(deviation)0 2274 y(is)31 b(0)p Fw(:)p FE(06.)46 b(The)31 b(correlation)f(co)r(e\016cien)n(t)h(b)r(et)n(w)n(een)g (measured)f(and)h(estimated)g(calls)g(is)g(0)p Fw(:)p FE(99.)46 b(The)31 b(net)n(w)n(orks)f(in)h Ff(Set-A)0 2374 y FE(w)n(ere)c(used)g(in)h(this)g(exp)r(erimen)n(ts|see)f(App)r (endix)h(A.)0 2635 y(This)i(theorem)g(is)g(quite)h(imp)r(ortan)n(t)f (practically)f(as)h(it)h(allo)n(ws)e(one)h(to)g(estimate)g(the)h (running)f(time)h(of)f Ff(r)n(c)h FE(under)f(an)n(y)0 2735 y(giv)n(en)f(memory)g(con\014guration.)43 b(All)30 b(w)n(e)g(ha)n(v)n(e)e(to)i(do)g(is)g(add)f(up)i Fu(ave)p FE(\()p Fw(T)12 b FE(\))29 b(for)h(ev)n(ery)e(no)r(de)i Fw(T)42 b FE(in)30 b(the)g(dtree.)44 b(Note)30 b(that)0 2834 y(once)h Fu(ave)p FE(\()p Fw(T)401 2804 y Fj(p)438 2834 y FE(\))h(is)f(computed,)h(w)n(e)f(can)f(compute)h Fu(ave)q FE(\()p Fw(T)12 b FE(\))30 b(in)i(constan)n(t)e(time.)48 b(Therefore,)31 b(w)n(e)f(can)h(compute)g(and)g(sum)0 2934 y Fu(ave)p FE(\()p Fw(T)12 b FE(\))27 b(for)g(ev)n(ery)g(no)r(de)g Fw(T)39 b FE(in)28 b(the)g(dtree)f(in)h(time)g(linear)f(in)h(the)g (dtree)f(size.)125 3033 y(Before)32 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mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Latex) findfont 160 scalefont setfont 1.000 UL LTb 624 480 M 63 0 V 6241 0 R -63 0 V 528 480 M (15) Rshow 624 1296 M 63 0 V 6241 0 R -63 0 V -6337 0 R (20) Rshow 624 2112 M 63 0 V 6241 0 R -63 0 V -6337 0 R (25) Rshow 624 2928 M 63 0 V 6241 0 R -63 0 V -6337 0 R (30) Rshow 624 3744 M 63 0 V 6241 0 R -63 0 V -6337 0 R (35) Rshow 624 4560 M 63 0 V 6241 0 R -63 0 V -6337 0 R (40) Rshow 624 480 M 0 63 V 0 4017 R 0 -63 V 624 320 M (0) Cshow 1018 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (1) Cshow 1412 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (2) Cshow 1806 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (3) Cshow 2200 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (4) Cshow 2594 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (5) Cshow 2988 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (6) Cshow 3382 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (7) Cshow 3776 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (8) Cshow 4170 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (9) Cshow 4564 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (10) Cshow 4958 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (11) Cshow 5352 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (12) Cshow 5746 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (13) Cshow 6140 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (14) Cshow 6534 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (15) Cshow 6928 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (16) Cshow 1.000 UL LTb 624 480 M 6304 0 V 0 4080 V -6304 0 V 624 480 L 160 2520 M currentpoint gsave translate 90 rotate 0 0 M (Recursive Calls Width) Cshow grestore 3776 80 M (Cache Width) Cshow 3776 4800 M (PIGS Network) Cshow 1.000 UP 1.000 UL LT0 6193 4417 M (balanced dtree) Rshow 6289 4417 M 447 0 V 624 3909 M 39 -14 V 40 -15 V 39 -17 V 40 -19 V 39 -22 V 39 -23 V 40 -27 V 39 -30 V 40 -35 V 39 -28 V 39 -11 V 40 -12 V 39 -13 V 40 -14 V 39 -15 V 39 -17 V 40 -18 V 39 -20 V 40 -22 V 39 -24 V 39 -27 V 40 -30 V 39 -34 V 40 -38 V 39 -19 V 39 -15 V 40 -18 V 39 -18 V 40 -21 V 39 -22 V 39 -25 V 40 -27 V 39 -30 V 40 -34 V 39 -37 V 39 -39 V 40 -20 V 39 -23 V 40 -26 V 39 -30 V 39 -35 V 40 -31 V 39 -11 V 40 -11 V 39 -13 V 39 -14 V 40 -15 V 39 -17 V 40 -19 V 39 -21 V 39 -23 V 40 -27 V 39 -30 V 40 -34 V 39 -40 V 39 -13 V 40 -13 V 39 -14 V 40 -15 V 39 -17 V 39 -18 V 40 -20 V 39 -23 V 40 -15 V 39 -2 V 39 -3 V 40 -3 V 39 -3 V 40 -4 V 39 -3 V 39 -4 V 40 -5 V 39 -5 V 40 -5 V 39 -6 V 39 -6 V 40 -7 V 39 -8 V 40 -8 V 39 -10 V 39 -10 V 40 -11 V 39 -13 V 40 -15 V 39 -16 V 39 -19 V 40 -21 V 39 -25 V 40 -30 V 39 -10 V 39 -2 V 40 -2 V 39 -3 V 40 -2 V 39 -3 V 39 -3 V 40 -3 V 39 -4 V 40 -3 V 39 -5 V 39 -4 V 40 -5 V 39 -5 V 40 -5 V 39 -6 V 39 -7 V 40 -7 V 39 -8 V 40 -9 V 39 -9 V 39 -10 V 40 -12 V 39 -13 V 40 -14 V 39 -15 V 39 -18 V 40 -20 V 39 -22 V 40 -18 V 39 0 V 39 -1 V 40 0 V 39 0 V 40 -1 V 39 0 V 39 -1 V 40 -1 V 39 0 V 40 -1 V 39 -1 V 39 -1 V 40 -1 V 39 -1 V 40 -1 V 39 -1 V 39 -1 V 40 -1 V 39 -2 V 40 -1 V 39 -2 V 39 -1 V 40 -2 V 39 -2 V 40 -2 V 39 -3 V 39 -2 V 40 -3 V 39 -3 V 40 -4 V 39 -3 V 39 -4 V 40 -4 V 39 -5 V 40 -5 V 39 -5 V 39 -7 V 40 -6 V 39 -8 V 40 -8 V 39 -9 V 624 3909 TriU 663 3895 TriU 703 3880 TriU 742 3863 TriU 782 3844 TriU 821 3822 TriU 860 3799 TriU 900 3772 TriU 939 3742 TriU 979 3707 TriU 1018 3679 TriU 1057 3668 TriU 1097 3656 TriU 1136 3643 TriU 1176 3629 TriU 1215 3614 TriU 1254 3597 TriU 1294 3579 TriU 1333 3559 TriU 1373 3537 TriU 1412 3513 TriU 1451 3486 TriU 1491 3456 TriU 1530 3422 TriU 1570 3384 TriU 1609 3365 TriU 1648 3350 TriU 1688 3332 TriU 1727 3314 TriU 1767 3293 TriU 1806 3271 TriU 1845 3246 TriU 1885 3219 TriU 1924 3189 TriU 1964 3155 TriU 2003 3118 TriU 2042 3079 TriU 2082 3059 TriU 2121 3036 TriU 2161 3010 TriU 2200 2980 TriU 2239 2945 TriU 2279 2914 TriU 2318 2903 TriU 2358 2892 TriU 2397 2879 TriU 2436 2865 TriU 2476 2850 TriU 2515 2833 TriU 2555 2814 TriU 2594 2793 TriU 2633 2770 TriU 2673 2743 TriU 2712 2713 TriU 2752 2679 TriU 2791 2639 TriU 2830 2626 TriU 2870 2613 TriU 2909 2599 TriU 2949 2584 TriU 2988 2567 TriU 3027 2549 TriU 3067 2529 TriU 3106 2506 TriU 3146 2491 TriU 3185 2489 TriU 3224 2486 TriU 3264 2483 TriU 3303 2480 TriU 3343 2476 TriU 3382 2473 TriU 3421 2469 TriU 3461 2464 TriU 3500 2459 TriU 3540 2454 TriU 3579 2448 TriU 3618 2442 TriU 3658 2435 TriU 3697 2427 TriU 3737 2419 TriU 3776 2409 TriU 3815 2399 TriU 3855 2388 TriU 3894 2375 TriU 3934 2360 TriU 3973 2344 TriU 4012 2325 TriU 4052 2304 TriU 4091 2279 TriU 4131 2249 TriU 4170 2239 TriU 4209 2237 TriU 4249 2235 TriU 4288 2232 TriU 4328 2230 TriU 4367 2227 TriU 4406 2224 TriU 4446 2221 TriU 4485 2217 TriU 4525 2214 TriU 4564 2209 TriU 4603 2205 TriU 4643 2200 TriU 4682 2195 TriU 4722 2190 TriU 4761 2184 TriU 4800 2177 TriU 4840 2170 TriU 4879 2162 TriU 4919 2153 TriU 4958 2144 TriU 4997 2134 TriU 5037 2122 TriU 5076 2109 TriU 5116 2095 TriU 5155 2080 TriU 5194 2062 TriU 5234 2042 TriU 5273 2020 TriU 5313 2002 TriU 5352 2002 TriU 5391 2001 TriU 5431 2001 TriU 5470 2001 TriU 5510 2000 TriU 5549 2000 TriU 5588 1999 TriU 5628 1998 TriU 5667 1998 TriU 5707 1997 TriU 5746 1996 TriU 5785 1995 TriU 5825 1994 TriU 5864 1993 TriU 5904 1992 TriU 5943 1991 TriU 5982 1990 TriU 6022 1989 TriU 6061 1987 TriU 6101 1986 TriU 6140 1984 TriU 6179 1983 TriU 6219 1981 TriU 6258 1979 TriU 6298 1977 TriU 6337 1974 TriU 6376 1972 TriU 6416 1969 TriU 6455 1966 TriU 6495 1962 TriU 6534 1959 TriU 6573 1955 TriU 6613 1951 TriU 6652 1946 TriU 6692 1941 TriU 6731 1936 TriU 6770 1929 TriU 6810 1923 TriU 6849 1915 TriU 6889 1907 TriU 6928 1898 TriU 6512 4417 TriU 1.000 UP 1.000 UL LT1 6193 4257 M (unbalanced dtree) Rshow 6289 4257 M 447 0 V 624 4418 M 197 -90 V 197 -159 V 197 -185 V 197 -41 V 197 -60 V 197 -91 V 197 -143 V 197 -81 V 197 -120 V 197 -192 V 197 -211 V 197 -118 V 197 -56 V 197 -93 V 197 -123 V 197 -60 V 197 -96 V 197 -131 V 197 -67 V 197 -99 V 197 -148 V 197 -131 V 197 -164 V 197 -256 V 197 -343 V 197 -108 V 197 -74 V 197 -97 V 197 -80 V 197 -49 V 197 -33 V 197 -5 V 624 4418 CircleF 821 4328 CircleF 1018 4169 CircleF 1215 3984 CircleF 1412 3943 CircleF 1609 3883 CircleF 1806 3792 CircleF 2003 3649 CircleF 2200 3568 CircleF 2397 3448 CircleF 2594 3256 CircleF 2791 3045 CircleF 2988 2927 CircleF 3185 2871 CircleF 3382 2778 CircleF 3579 2655 CircleF 3776 2595 CircleF 3973 2499 CircleF 4170 2368 CircleF 4367 2301 CircleF 4564 2202 CircleF 4761 2054 CircleF 4958 1923 CircleF 5155 1759 CircleF 5352 1503 CircleF 5549 1160 CircleF 5746 1052 CircleF 5943 978 CircleF 6140 881 CircleF 6337 801 CircleF 6534 752 CircleF 6731 719 CircleF 6928 714 CircleF 6512 4257 CircleF stroke grestore end showpage %%Trailer %%DocumentFonts: Latex %%EndDocument @endspecial 1615 x @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2551 @rwi @setspecial %%BeginDocument: munin2.ps %!PS-Adobe-2.0 EPSF-2.0 %%Title: c:/windows/desktop/rc/loop-cutset/munin2.ps %%Creator: gnuplot 3.7 patchlevel 0 %%CreationDate: Fri Aug 13 14:20:14 1999 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -53 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def 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2253 TriU 3220 2249 TriU 3257 2244 TriU 3294 2238 TriU 3331 2232 TriU 3368 2226 TriU 3405 2219 TriU 3442 2211 TriU 3479 2203 TriU 3516 2194 TriU 3554 2184 TriU 3591 2174 TriU 3628 2162 TriU 3665 2149 TriU 3702 2136 TriU 3739 2120 TriU 3776 2103 TriU 3813 2085 TriU 3850 2074 TriU 3887 2070 TriU 3924 2067 TriU 3961 2063 TriU 3998 2058 TriU 4036 2054 TriU 4073 2049 TriU 4110 2044 TriU 4147 2038 TriU 4184 2032 TriU 4221 2025 TriU 4258 2018 TriU 4295 2011 TriU 4332 2003 TriU 4369 1994 TriU 4406 1986 TriU 4443 1976 TriU 4481 1966 TriU 4518 1956 TriU 4555 1946 TriU 4592 1936 TriU 4629 1926 TriU 4666 1917 TriU 4703 1908 TriU 4740 1898 TriU 4777 1887 TriU 4814 1874 TriU 4851 1859 TriU 4888 1841 TriU 4926 1831 TriU 4963 1826 TriU 5000 1821 TriU 5037 1815 TriU 5074 1808 TriU 5111 1801 TriU 5148 1794 TriU 5185 1785 TriU 5222 1776 TriU 5259 1766 TriU 5296 1755 TriU 5333 1742 TriU 5371 1728 TriU 5408 1712 TriU 5445 1694 TriU 5482 1673 TriU 5519 1649 TriU 5556 1621 TriU 5593 1586 TriU 5630 1543 TriU 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CircleF 995 4390 CircleF 1180 4364 CircleF 1366 4323 CircleF 1551 4254 CircleF 1736 4202 CircleF 1922 4150 CircleF 2107 4062 CircleF 2293 3859 CircleF 2478 3324 CircleF 2664 3181 CircleF 2849 3006 CircleF 3034 2860 CircleF 3220 2616 CircleF 3405 1983 CircleF 3591 1928 CircleF 3776 1841 CircleF 3961 1694 CircleF 4147 1458 CircleF 4332 1342 CircleF 4518 1320 CircleF 4703 1285 CircleF 4888 1218 CircleF 5074 1128 CircleF 5259 1073 CircleF 5445 980 CircleF 5630 964 CircleF 5816 941 CircleF 6001 918 CircleF 6186 912 CircleF 6372 912 CircleF 6557 912 CircleF 6743 912 CircleF 6928 912 CircleF 6512 4257 CircleF stroke grestore end showpage %%Trailer %%DocumentFonts: Latex %%EndDocument @endspecial 1614 x @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2551 @rwi @setspecial %%BeginDocument: diabetes.ps %!PS-Adobe-2.0 EPSF-2.0 %%Title: c:/windows/desktop/rc/loop-cutset/diabetes.ps %%Creator: gnuplot 3.7 patchlevel 0 %%CreationDate: Fri Aug 13 14:20:12 1999 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -53 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 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@setspecial %%BeginDocument: contract.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: contract.eps %%Creator: fig2dev Version 3.2 Patchlevel 0-beta3 %%CreationDate: Mon Jul 26 18:06:13 1999 %%For: darwiche@localhost.localdomain (Adnan Darwiche,,,,) %%Orientation: Portrait %%BoundingBox: 0 0 738 144 %%Pages: 0 %%BeginSetup %%EndSetup %%Magnification: 1.0000 %%EndComments /MyAppDict 100 dict dup begin def /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save -8.0 383.0 translate 1 -1 scale .9 .9 scale % to make patterns same scale as in xfig % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index show % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proe char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % this is the pattern fill program from the Second edition Reference Manual % with changes to call the above pattern fill % left30 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 32 16 true [ 32 0 0 -16 0 16 ] {} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P1 exch def 1.1111 1.1111 scale %restore scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def %%EndProlog $F2psBegin 10 setmiterlimit n -1000 7375 m -1000 -1000 l 13423 -1000 l 13423 7375 l cp clip 0.06000 0.06000 sc 7.500 slw % Ellipse n 255 4515 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 14.47 298.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 840 4245 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 53.47 280.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 1455 4560 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 94.47 301.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 855 4830 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 54.47 319.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 2040 4845 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 133.47 320.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 1455 5145 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 94.47 340.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 2655 5145 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 174.47 340.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 2040 5430 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 133.47 359.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 3240 5445 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 213.47 360.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 2670 5715 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 175.47 378.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 3270 6015 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 215.47 398.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 3855 5745 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 254.47 380.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 3885 6315 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 256.47 418.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 4463 6060 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 295.00 401.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 5033 6330 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 333.00 419.47] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline 15.000 slw n 5040 6330 m 825 4245 l gs col0 s gr % Polyline n 840 4245 m 225 4530 l gs col0 s gr % Polyline n 1440 4560 m 840 4845 l gs col0 s gr % Polyline n 2040 4845 m 1425 5160 l gs col0 s gr % Polyline n 2640 5145 m 2025 5445 l gs col0 s gr % Polyline n 3255 5445 m 2640 5730 l gs col0 s gr % Polyline n 3840 5745 m 3240 6045 l gs col0 s gr % Polyline n 4440 6030 m 3855 6345 l gs col0 s gr /Times-Roman ff 180.00 scf sf 795 4170 m gs 1 -1 sc (A) col0 sh gr /Times-Roman ff 180.00 scf sf 135 4485 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 180.00 scf sf 1470 4515 m gs 1 -1 sc (C) col0 sh gr /Times-Roman ff 180.00 scf sf 720 4800 m gs 1 -1 sc (D) col0 sh gr /Times-Roman ff 180.00 scf sf 2055 4755 m gs 1 -1 sc (E) col0 sh gr /Times-Roman ff 180.00 scf sf 1320 5085 m gs 1 -1 sc (F) col0 sh gr /Times-Roman ff 180.00 scf sf 2640 5070 m gs 1 -1 sc (G) col0 sh gr /Times-Roman ff 180.00 scf sf 1890 5370 m gs 1 -1 sc (H) col0 sh gr /Times-Roman ff 180.00 scf sf 3270 5370 m gs 1 -1 sc (I) col0 sh gr /Times-Roman ff 180.00 scf sf 2520 5715 m gs 1 -1 sc (J) col0 sh gr /Times-Roman ff 180.00 scf sf 3825 5670 m gs 1 -1 sc (K) col0 sh gr /Times-Roman ff 180.00 scf sf 3165 5985 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 180.00 scf sf 4455 6000 m gs 1 -1 sc (M) col0 sh gr /Times-Roman ff 180.00 scf sf 3735 6270 m gs 1 -1 sc (N) col0 sh gr /Times-Roman ff 180.00 scf sf 5025 6270 m gs 1 -1 sc (O) col0 sh gr 7.500 slw % Ellipse n 9615 4830 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 638.47 319.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 10230 5145 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 679.47 340.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 10815 5430 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 718.47 359.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 11415 5730 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 758.47 379.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 12015 6015 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 798.47 398.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 4710 4230 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 311.47 279.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 5325 4530 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 352.47 299.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 5940 4815 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 393.47 318.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 6555 5130 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 434.47 339.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 7140 5415 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 473.47 358.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 7740 5715 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 513.47 378.47] PATmp PATsp ef gr PATusp gs col0 s gr % Ellipse n 8340 6000 38 38 0 360 DrawEllipse gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 553.47 397.47] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline 15.000 slw n 12030 6030 m 9585 4815 l gs col0 s gr % Polyline n 8355 6015 m 4665 4200 l gs col0 s gr % Polyline 30.000 slw gs clippath 4524 5010 m 4884 5100 l 4524 5190 l 5010 5190 l 5010 5010 l cp clip n 4065 5100 m 4965 5100 l gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 271.00 340.00] PATmp PATsp ef gr PATusp gs col0 s gr gr % arrowhead n 4524 5010 m 4884 5100 l 4524 5190 l col0 s % Polyline gs clippath 8394 4995 m 8754 5085 l 8394 5175 l 8880 5175 l 8880 4995 l cp clip n 7935 5085 m 8835 5085 l gs /PC [[0.00 0.00 0.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P1 [16 0 0 -8 529.00 339.00] PATmp PATsp ef gr PATusp gs col0 s gr gr % arrowhead n 8394 4995 m 8754 5085 l 8394 5175 l col0 s /Times-Roman ff 180.00 scf sf 10785 5340 m gs 1 -1 sc (I) col0 sh gr /Times-Roman ff 180.00 scf sf 11340 5640 m gs 1 -1 sc (K) col0 sh gr /Times-Roman ff 180.00 scf sf 11970 5970 m gs 1 -1 sc (M) col0 sh gr /Times-Roman ff 180.00 scf sf 12135 5970 m gs 1 -1 sc (N) col0 sh gr /Times-Roman ff 180.00 scf sf 11475 5640 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 180.00 scf sf 10860 5340 m gs 1 -1 sc (J) col0 sh gr /Times-Roman ff 180.00 scf sf 12285 5970 m gs 1 -1 sc (O) col0 sh gr /Times-Roman ff 180.00 scf sf 4635 4125 m gs 1 -1 sc (A) col0 sh gr /Times-Roman ff 180.00 scf sf 5310 4470 m gs 1 -1 sc (C) col0 sh gr /Times-Roman ff 180.00 scf sf 5895 4710 m gs 1 -1 sc (E) col0 sh gr /Times-Roman ff 180.00 scf sf 6480 5025 m gs 1 -1 sc (G) col0 sh gr /Times-Roman ff 180.00 scf sf 7110 5325 m gs 1 -1 sc (I) col0 sh gr /Times-Roman ff 180.00 scf sf 7665 5625 m gs 1 -1 sc (K) col0 sh gr /Times-Roman ff 180.00 scf sf 8295 5955 m gs 1 -1 sc (M) col0 sh gr /Times-Roman ff 180.00 scf sf 4785 4125 m gs 1 -1 sc (B) col0 sh gr /Times-Roman ff 180.00 scf sf 6600 5025 m gs 1 -1 sc (H) col0 sh gr /Times-Roman ff 180.00 scf sf 8460 5955 m gs 1 -1 sc (N) col0 sh gr /Times-Roman ff 180.00 scf sf 7800 5625 m gs 1 -1 sc (L) col0 sh gr /Times-Roman ff 180.00 scf sf 5415 4470 m gs 1 -1 sc (D) col0 sh gr /Times-Roman ff 180.00 scf sf 7185 5325 m gs 1 -1 sc (J) col0 sh gr /Times-Roman ff 180.00 scf sf 6015 4710 m gs 1 -1 sc (F) col0 sh gr /Times-Roman ff 180.00 scf sf 8610 5955 m gs 1 -1 sc (O) col0 sh gr /Times-Roman ff 180.00 scf sf 9675 4785 m gs 1 -1 sc (ABCD) col0 sh gr /Times-Roman ff 180.00 scf sf 10305 5100 m gs 1 -1 sc (EFGH) col0 sh gr /Times-Roman ff 180.00 scf sf 7785 4875 m gs 1 -1 sc (COMPRESS) col0 sh gr /Times-Roman ff 180.00 scf sf 4185 4920 m gs 1 -1 sc (RAKE) col0 sh gr $F2psEnd rs end %%EndDocument @endspecial 852 1047 a FE(Figure)27 b(17:)36 b(Demonstrating)26 b(the)i Ff(contra)n(ct)g FE(op)r(eration)f(of)g([24)o(].)p 543 1254 2815 4 v 543 2058 4 805 v 1161 1337 a Ft(Algorithm)j Ff(bal-dt)p 1161 1366 736 4 v 599 1505 a(bal-dt)p FE(\()p Fw(T)12 b FE(\))647 1605 y(for)27 b(eac)n(h)g(in)n(ternal)g(no)r(de)g Fw(N)37 b FE(in)28 b Fw(T)12 b FE(,)27 b Ff(label)o FE(\()p Fw(N)9 b FE(\))19 b Fv( )65 b FE(empt)n(y)27 b(dtree)647 1705 y(for)g(eac)n(h)g(leaf)g(no)r(de)h Fw(N)36 b FE(in)28 b Fw(T)12 b FE(,)27 b Ff(label)p FE(\()p Fw(N)9 b FE(\))18 b Fv( )65 b FE(dtree)27 b(N)647 1804 y Ff(op)19 b Fv( )36 b Ff(compose)647 1904 y Fw(R)19 b Fv( )37 b FE(\014nal)28 b(no)r(de)f(resulting)g(from)g(successiv)n(e)g(applications)f(of)i Ff(contra)n(ct)g FE(to)f Fw(T)647 2004 y FE(return)g Ff(label)p FE(\()p Fw(R)q FE(\))p 3354 2058 4 805 v 543 2061 2815 4 v 1113 2211 a(Figure)g(18:)36 b(Pseudo)r(co)r(de)27 b(for)g(balancing)g(a)g(dtree.)0 2559 y(soundness)g(is)g(established)h (b)r(elo)n(w:)0 2725 y Ft(Theorem)i(8)42 b Fx(L)l(et)29 b Fv(N)43 b Fx(b)l(e)30 b(a)h(Bayesian)h(network)e(and)h(let)f Fw(\031)j Fx(b)l(e)e(a)f(c)l(orr)l(esp)l(onding)i(elimination)f(or)l (der)g(of)g(width)g Fw(w)r Fx(.)41 b(The)0 2825 y(c)l(al)t(l)31 b Ff(el2dt)o FE(\()p Fv(N)12 b Fw(;)i(\031)s FE(\))31 b Fx(wil)t(l)g(r)l(eturn)e(a)h(dtr)l(e)l(e)g(of)g(width)h Fv(\024)23 b Fw(w)32 b Fx(for)f(network)e Fv(N)12 b Fx(.)0 3057 y Fb(6.3)112 b(Balancing)37 b(Dtrees)0 3210 y FE(W)-7 b(e)31 b(no)n(w)f(presen)n(t)g(an)g(algorithm)g(for)g(balancing)g(a)g (dtree)g(while)h(increasing)e(its)i(width)g(b)n(y)g(no)f(more)g(than)h (a)f(constan)n(t)0 3310 y(factor.)k(The)22 b(algorithm)e(is)h(similar)g (to)h Ff(el2dt)f FE(except)h(that)f(the)h(comp)r(osition)f(pro)r(cess)g (is)g(not)h(driv)n(en)f(b)n(y)g(an)g(elimination)0 3409 y(order.)56 b(Instead,)36 b(it)e(is)h(driv)n(en)e(b)n(y)h(applying)g (the)h Ff(contra)n(ct)f FE(op)r(eration)g(of)g([24)o(])h(to)f(the)h (giv)n(en)e(dtree.)57 b(W)-7 b(e)35 b(need)f(to)0 3509 y(explain)27 b(this)h(op)r(eration)f(\014rst.)125 3609 y Ff(contra)n(ct)e FE(is)h(an)f(op)r(eration)g(whic)n(h)h(is)f(applied) h(to)g(a)f(tree.)36 b(It)26 b(simply)g Fx(absorbs)h FE(some)e(of)h(the) g(tree)f(no)r(des)h(in)n(to)f(their)0 3708 y(neigh)n(b)r(ors,)31 b(therefore,)g(pro)r(ducing)g(a)g(smaller)f(tree.)48 b(T)-7 b(o)31 b(absorb)f(no)r(de)h Fw(N)2414 3720 y Fq(1)2482 3708 y FE(in)n(to)g(no)r(de)h Fw(N)2926 3720 y Fq(2)2994 3708 y FE(is)f(to)g(mak)n(e)g(the)g(neigh)n(b)r(ors)0 3808 y(of)h Fw(N)166 3820 y Fq(1)236 3808 y FE(in)n(to)g(neigh)n(b)r (ors)f(of)i Fw(N)955 3820 y Fq(2)1024 3808 y FE(and)f(to)h(remo)n(v)n (e)e(no)r(de)h Fw(N)1858 3820 y Fq(1)1927 3808 y FE(from)h(the)f(tree.) 52 b Ff(contra)n(ct)32 b FE(w)n(orks)f(b)n(y)h(applying)g(a)g Ff(rake)0 3908 y FE(op)r(eration)22 b(to)i(the)f(tree,)h(follo)n(w)n (ed)f(b)n(y)g(a)g Ff(compress)g FE(op)r(eration.)35 b(The)23 b Ff(rake)h FE(op)r(eration)e(is)h(simple:)35 b(it)24 b(absorbs)e(eac)n(h)g(leaf)0 4007 y(no)r(de)j(in)n(to)f(its)h(paren)n (t.)35 b(The)25 b Ff(compress)g FE(op)r(eration)e(is)i(more)f(in)n(v)n (olv)n(ed:)34 b(it)25 b(iden)n(ti\014es)f(maximal)g(c)n(hains)g Fw(N)3430 4019 y Fq(1)3467 4007 y Fw(;)14 b(N)3571 4019 y Fq(2)3608 4007 y Fw(;)g(:)g(:)g(:)g(;)g(N)3860 4019 y Fj(k)0 4107 y FE(and)26 b(then)g(absorbs)e Fw(N)713 4119 y Fj(i)766 4107 y FE(in)n(to)i Fw(N)1000 4119 y Fj(i)p Fq(+1)1137 4107 y FE(for)f(o)r(dd)h Fw(i)p FE(.)36 b(The)26 b(sequence)f Fw(N)2090 4119 y Fq(1)2127 4107 y Fw(;)14 b(N)2231 4119 y Fq(2)2268 4107 y Fw(;)g(:)g(:)g(:)g(;)g(N) 2520 4119 y Fj(k)2586 4107 y FE(is)26 b(a)f(c)n(hain)g(if)i Fw(N)3094 4119 y Fj(i)p Fq(+1)3231 4107 y FE(is)f(the)g(only)f(c)n (hild)h(of)0 4206 y Fw(N)67 4218 y Fj(i)124 4206 y FE(for)j(1)d Fv(\024)g Fw(i)g(<)g(k)s FE(,)31 b(and)e(if)h Fw(N)966 4218 y Fj(k)1036 4206 y FE(has)g(exactly)f(one)g(c)n(hild)h(and)f(that) h(c)n(hild)g(is)f(not)h(a)f(leaf.)43 b(T)n(ypically)-7 b(,)29 b(eac)n(h)g(tree)h(no)r(de)f Fw(N)0 4306 y FE(will)24 b(ha)n(v)n(e)f(an)g(application{sp)r(eci\014c)g(lab)r(el,)h Ff(label)p FE(\()p Fw(N)9 b FE(\).)36 b(When)24 b(no)r(de)g Fw(N)2332 4318 y Fq(1)2393 4306 y FE(is)f(absorb)r(ed)g(in)n(to)h(its)g (neigh)n(b)r(or)e Fw(N)3503 4318 y Fq(2)3540 4306 y FE(,)j(the)f(lab)r (el)0 4406 y(of)29 b Fw(N)163 4418 y Fq(2)230 4406 y FE(is)g(up)r(dated)h(as)f(follo)n(ws:)39 b Ff(label)p FE(\()p Fw(N)1384 4418 y Fq(2)1421 4406 y FE(\))19 b Fv( )37 b Ff(label)p FE(\()p Fw(N)1922 4418 y Fq(1)1959 4406 y FE(\))52 b Ff(op)h(label)o FE(\()p Fw(N)2524 4418 y Fq(2)2561 4406 y FE(\))30 b(where)f Ff(op)h FE(is)f(an)g (application{sp)r(eci\014c)0 4505 y(op)r(eration.)50 b(One)32 b(of)h(the)f(k)n(ey)g(applications)g(of)g Ff(contra)n(ct)h FE(is)f(in)g(ev)-5 b(aluating)32 b(arithmetic{expression)e(trees.)51 b(In)33 b(this)0 4605 y(application,)27 b(the)h(lab)r(el)g(of)f(a)g(no) r(de)h(is)f(a)h(n)n(um)n(b)r(er)f(and)g(the)h(op)r(eration)f Ff(op)h FE(is)f(either)h(addition)f(or)g(m)n(ultiplication.)125 4705 y(Figure)d(17)g(depicts)i(an)e(example)h(where)g Ff(contra)n(ct)g FE(is)g(applied)g(to)g(a)g(tree,)g(where)g(the)g(lab)r (els)g(of)g(no)r(des)g(are)f(strings)0 4804 y(and)h Ff(op)g FE(is)g(string)g(concatenation.)35 b(The)25 b(main)g(prop)r(ert)n(y)f (of)h Ff(contra)n(ct)h FE(is)f(that)g(an)n(y)g(tree)g(can)f(b)r(e)i (reduced)f(to)g(a)g(single)0 4904 y(no)r(de)j(b)n(y)f(only)g(applying)g Ff(contra)n(ct)h Fw(O)r FE(\(log)15 b Fw(n)p FE(\))28 b(times,)g(where)f Fw(n)g FE(the)h(size)f(of)h(giv)n(en)f(tree)g([24)o (].)125 5003 y(W)-7 b(e)34 b(will)g(use)g Ff(contra)n(ct)h FE(to)f(balance)f(a)h(dtree)g Fw(T)45 b FE(as)34 b(follo)n(ws.)55 b(First,)36 b(w)n(e)e(lab)r(el)g(eac)n(h)f(in)n(ternal)h(no)r(de)g(in)g Fw(T)46 b FE(with)0 5103 y(the)31 b(empt)n(y)f(dtree.)44 b(Second,)31 b(w)n(e)e(lab)r(el)h(eac)n(h)g(leaf)g(no)r(de)g(of)g Fw(T)41 b FE(with)31 b(itself.)45 b(W)-7 b(e)30 b(then)h(c)n(ho)r(ose)e (the)h(op)r(eration)f Ff(op)i FE(to)f(b)r(e)0 5203 y Ff(compose)p FE(,)36 b(de\014ned)f(in)g(Section)f(6.2.)56 b(Finally)-7 b(,)36 b(w)n(e)e(apply)g Ff(contra)n(ct)h FE(successiv)n(ely)e(to)h Fw(T)45 b FE(un)n(til)35 b(it)g(is)f(reduced) g(to)g(a)0 5302 y(single)23 b(no)r(de)h(and)g(return)g(the)g(lab)r(el)g (of)g(the)g(\014nal)g(no)r(de.)36 b(This)24 b(algorithm)e(is)i(giv)n (en)f(in)i(Figure)e(18.)35 b(Its)24 b(prop)r(erties)f(follo)n(w:)1908 5656 y(19)p eop %%Page: 20 20 20 19 bop 0 90 a Ft(Theorem)30 b(9)42 b Fx(L)l(et)31 b Fw(T)42 b Fx(b)l(e)31 b(a)h(dtr)l(e)l(e)f(of)i(c)l(ontext)d(width)i Fw(w)i Fx(for)e(a)g(Bayesian)h(network)f Fv(N)43 b Fx(with)32 b Fw(n)g Fx(no)l(des.)43 b Ff(bal-dt)p Fx(\()p Fw(T)12 b Fx(\))31 b(wil)t(l)0 190 y(take)e Fw(O)r FE(\()p Fw(n)14 b FE(log)h Fw(n)p FE(\))29 b Fx(time)h(and)f(wil)t(l)i(r)l(eturn)d(a)h (dtr)l(e)l(e)g(for)h Fv(N)42 b Fx(of)30 b(height)g Fw(O)r FE(\(log)15 b Fw(n)p FE(\))p Fx(,)30 b(cutset)e(width)i Fv(\024)23 b Fw(w)r Fx(,)30 b(c)l(ontext)e(width)i Fv(\024)23 b FE(2)p Fw(w)0 289 y Fx(and)30 b(width)h Fv(\024)23 b FE(3)p Fw(w)d Fv(\000)e FE(1)p Fx(.)0 472 y FE(The)23 b(exp)r(erimen)n(tal)f(results)g(in)h(App)r(endix)h(A)f(pro)n(vide)f(a) g(sense)g(of)h(the)g(constan)n(t)f(factors)g(in)n(v)n(olv)n(ed)f(in)i (this)g(theorem.)35 b(F)-7 b(or)0 572 y(example,)30 b(the)g(width)g(is) f(increased)g(b)n(y)g(2)p Fw(:)p FE(1)g(for)g Ff(Set-A)g FE(net)n(w)n(orks)f(and)i(b)n(y)f(1)p Fw(:)p FE(6)g(for)g Ff(Set-B)h FE(net)n(w)n(orks)e(after)h(balancing)0 671 y(using)e(algorithm)g Ff(bal-dt)p FE(.)125 771 y(The)f(imp)r(ortan)n(t) g(asp)r(ect)g(of)g(Theorem)g(9)g(is)g(that)h(balancing)e(a)h(dtree)g (will)h(increase)e(eac)n(h)g(of)i(its)f(widths)h(b)n(y)f(no)g(more)0 871 y(than)32 b(a)g(constan)n(t)f(factor.)50 b(In)32 b(fact,)h(the)g(cutset)f(width)h(will)f(nev)n(er)f(exceed)h(the)h(con)n (text)e(width)i(of)f(un)n(balanced)f(dtree)0 970 y(after)c(applying)g Ff(bal-dt)p FE(.)0 1203 y Fb(6.4)112 b(Decomp)s(osition)36 b(b)m(y)h(Graph)i(Separators)0 1356 y FE(One)26 b(of)g(the)g(k)n(ey)f (di\013erences)h(b)r(et)n(w)n(een)g(recursiv)n(e)e(conditioning)i(and)g (previous)f(w)n(ork)f(on)i(nested)g(dissection)g(\(including)0 1456 y(the)32 b(w)n(ork)e(of)i(Co)r(op)r(er)f(on)h(recursiv)n(e)e (decomp)r(osition)h([3)o(]\))h(is)g(the)g(manner)f(in)h(whic)n(h)g(a)f (problem)h(is)f(decomp)r(osed)g(in)n(to)0 1555 y(smaller)19 b(problems,)i(and)g(the)f(formal)g(guaran)n(tees)e(pro)n(vided)h(on)i (the)f(qualit)n(y)g(of)g(suc)n(h)g(a)g(decomp)r(osition.)34 b(Previous)19 b(w)n(orks)0 1655 y(ha)n(v)n(e)32 b(app)r(ealed)h(to)g (the)h(notion)f(of)h Fx(gr)l(aph)i(sep)l(ar)l(ators)e FE(to)g(recursiv)n(ely)d(decomp)r(ose)i(a)g(graph)f(in)n(to)h(smaller)f (subgraphs)0 1754 y([14)o(].)43 b(A)30 b(graph)f(separator)e(is)i(a)h (set)f(of)h(no)r(des)f Ft(C)h FE(that)g(partitions)f(the)h(graph)e(in)n (to)h(three)h(sets)f Ft(A)p Fw(;)14 b Ft(B)p Fw(;)g Ft(C)p FE(,)30 b(suc)n(h)f(that)h(no)0 1854 y(no)r(de)f(in)h Ft(A)g FE(is)f(adjacen)n(t)g(to)h(a)f(no)r(de)g(in)h Ft(B)p FE(.)42 b(In)30 b(\014nding)g(separators,)d(one)i(tries)g(to)g (minimize)h(the)g(size)f(of)h(separator)d Ft(C)p FE(,)0 1954 y(while)i(k)n(eeping)e(the)i(sizes)f(of)g Ft(A)h FE(and)f Ft(B)h FE(as)e(close)h(as)g(p)r(ossible.)39 b(That)28 b(is,)h(the)f(emphasis)g(is)h(on)f(minimizing)h(separators,)0 2053 y(while)23 b(k)n(eeping)f(the)i(decomp)r(osition)e(balanced.)35 b(In)23 b(our)f(framew)n(ork,)g(this)h(corresp)r(onds)e(to)i (generating)e(balanced)i(dtrees)0 2153 y(that)32 b(ha)n(v)n(e)e(a)i (minimal)g(cutset)g(width.)50 b(But)32 b(this)g(do)r(es)f(not)h (necessarily)e(lead)h(to)h(minimizing)g(dtree)f(width,)j(whic)n(h)d(is) 0 2253 y(the)c(parameter)f(that)h(go)n(v)n(erns)d(the)j(complexit)n(y)f (of)h(recursiv)n(e)e(conditioning.)36 b(In)27 b(fact,)g(balanced)g (decomp)r(ositions)f(tend)0 2352 y(to)h(ha)n(v)n(e)g(larger)f(widths)i (than)f(un)n(balanced)g(ones.)125 2452 y(Cen)n(tral)d(to)i(the)g(w)n (ork)e(on)i(graph)e(separation)g(is)i(the)g(notion)f(of)h(an)f Fw(f)9 b FE(\()p Fw(n)p FE(\))p Fx({sep)l(ar)l(ator)30 b(the)l(or)l(em.)37 b FE(A)26 b(class)e(of)i(graphs)e(is)0 2551 y(said)i(to)g(ha)n(v)n(e)f(an)h Fw(f)9 b FE(\()p Fw(n)p FE(\){separator)23 b(theorem)j(i\013)g(there)g(exists)g(constan) n(ts)f Fw(\013)f(<)e FE(1)k(and)g Fw(\014)i(>)22 b FE(0)p Fw(;)k FE(suc)n(h)g(that)g(if)h Fw(G)f FE(is)g(a)g(graph)0 2651 y(in)g(the)g(class)e(with)i Fw(n)g FE(no)r(des,)g(then)g Fw(G)g FE(can)f(b)r(e)h(partitioned)f(in)n(to)g(sets)h Ft(A)p Fw(;)14 b Ft(B)p Fw(;)g Ft(C)25 b FE(suc)n(h)g(that)h(no)f(no)r (de)h(in)g Ft(A)g FE(is)f(adjacen)n(t)g(to)0 2751 y(a)i(no)r(de)h(in)g Ft(B)p FE(,)f(neither)h Ft(A)g FE(nor)f Ft(B)g FE(con)n(tains)g(more)g (than)g Fw(\013n)h FE(no)r(des,)g(and)f Ft(C)h FE(con)n(tains)e(no)i (more)e(than)i Fw(\014)t(f)9 b FE(\()p Fw(n)p FE(\))28 b(no)r(des.)125 2850 y(An)h Fw(f)9 b FE(\()p Fw(n)p FE(\){separator)26 b(theorem)i(for)h(a)f(class)g(of)h(graph)f(allo)n(ws)g(one)g(to)h (guaran)n(tee)e(the)i(qualit)n(y)g(of)g(recursiv)n(e)e(decom-)0 2950 y(p)r(ositions)33 b(obtained)g(for)g(that)h(class)f(of)g(graphs.) 54 b(F)-7 b(or)32 b(example,)j(planar)e(graphs)f(ha)n(v)n(e)2887 2890 y Fv(p)p 2956 2890 50 4 v 60 x Fw(n)p 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y(b)r(e)f(larger.)35 b(Note)28 b(that)f(computing)h(treewidth)g(is)f(an)h(NP{hard)e (problem.)125 4946 y(The)33 b(net)n(w)n(orks)f(w)n(ere)h(generated)g (randomly)g(as)g(follo)n(ws.)54 b(On)34 b(a)n(v)n(erage,)e(20\045)h(of) h(the)g(no)r(des)g(are)f(ro)r(ot,)h(10\045)f(ha)n(v)n(e)0 5046 y(a)g(single)h(paren)n(t,)g(20\045)g(ha)n(v)n(e)e(t)n(w)n(o)h (paren)n(ts,)i(25\045)e(ha)n(v)n(e)f(three)i(paren)n(ts,)h(20\045)e(ha) n(v)n(e)f(four)i(paren)n(ts)f(and)g(5\045)h(ha)n(v)n(e)e(\014v)n(e)0 5146 y(paren)n(ts.)43 b(W)-7 b(e)31 b(assumed)e(that)h(no)r(des)g(are)f (n)n(um)n(b)r(ered)h(from)g(0)f(to)h Fw(n)p FE(.)44 b(The)31 b(paren)n(ts)e(of)h(eac)n(h)f(no)r(de)h Fw(i)g FE(ha)n(v)n(e)f(b)r(een) h(c)n(hosen)0 5245 y(randomly)24 b(from)h(the)h(set)f(0)p Fw(;)14 b(:)g(:)g(:)f(;)h(i)g Fv(\000)g FE(1.)34 b(Moreo)n(v)n(er)22 b(an)n(y)j(paren)n(t)f(of)h(no)r(de)h Fw(i)f FE(w)n(as)f(not)h(to)g(b)r (e)h(less)e(than)i Fw(i)14 b Fv(\000)g Fw(w)26 b FE(for)f(a)g(certain)0 5345 y(constan)n(t)30 b Fw(w)r FE(.)46 b(This)31 b(constan)n(t)e(allo)n (ws)h(us)g(to)g(con)n(trol)g(the)h(connectivit)n(y)f(of)g(generated)f (net)n(w)n(ork;)i(the)g(bigger)e Fw(w)k FE(is,)f(the)1908 5656 y(21)p eop %%Page: 22 22 22 21 bop 0 90 a FE(more)33 b(connected)g(the)h(net)n(w)n(ork)e(is.)55 b(In)33 b(the)h(\014rst)f(set)h(of)f(net)n(w)n(orks,)h(w)n(e)f(c)n (hose)f Fw(w)37 b FE(randomly)32 b(for)h(eac)n(h)g(net)n(w)n(ork)f(so)h (it)0 190 y(ranges)26 b(b)r(et)n(w)n(een)i(2)f(and)g(35.)36 b(In)28 b(the)g(second)f(set,)h(it)g(ranged)e(b)r(et)n(w)n(een)h(2)h (and)f(75.)0 462 y Fy(B)134 b(Pro)t(ofs)0 644 y Ft(Lemma)30 b(1)41 b Fx(The)31 b(fol)t(lowing)h(r)l(elationships)f(hold:)56 798 y(\(a\))42 b Fu(cutset)o FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)h Fu(context)o FE(\()p Fw(T)12 b FE(\))23 b(=)g Fv(;)p Fx(.)60 958 y(\(b\))42 b Fu(context)o FE(\()p Fw(T)12 b FE(\))23 b Fv(\022)f Fu(cutset)p FE(\()p Fw(T)1001 928 y Fj(p)1039 958 y FE(\))c Fv([)h Fu(context)o FE(\()p Fw(T)1512 928 y Fj(p)1550 958 y FE(\))24 b(=)e Fu(cluster)q FE(\()p Fw(T)2014 928 y Fj(p)2052 958 y FE(\))p Fx(.)60 1118 y(\(c\))42 b Fu(cutset)o FE(\()p Fw(T)509 1088 y Fj(p)547 1118 y FE(\))23 b Fv(\022)g Fu(context)o FE(\()p Fw(T)12 b FE(\))p Fx(.)56 1278 y(\(d\))42 b Fu(cutset)o FE(\()p Fw(T)497 1290 y Fq(1)534 1278 y FE(\))19 b Fv(\\)g Fu(cutset)o FE(\()p Fw(T)948 1290 y Fq(2)985 1278 y FE(\))k(=)g Fv(;)29 b Fx(when)h Fw(T)1460 1290 y Fq(1)1527 1278 y Fx(is)g(an)g(anc)l(estor)g(of)g Fw(T)2211 1290 y Fq(2)2248 1278 y Fx(.)60 1438 y(\(e\))42 b Fu(context)o FE(\()p Fw(T)12 b FE(\))23 b(=)f Fu(cluster)q FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)h Fu(cluster)q FE(\()p Fw(T)1465 1408 y Fj(p)1503 1438 y FE(\))p Fx(.)0 1668 y Fb(Pro)s(of)37 b(of)h(Lemma)f(1)60 1821 y FE(\(a\))42 b(If)21 b Fw(X)30 b Fv(2)23 b Fu(context)p FE(\()p Fw(T)12 b FE(\),)22 b(then)g Fw(X)29 b Fv(2)23 b Fu(acutset)p FE(\()p Fw(T)12 b FE(\))21 b(since)g Fu(context)o FE(\()p Fw(T)12 b FE(\))23 b(=)g Fu(acutset)o FE(\()p Fw(T)12 b FE(\))6 b Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\).)34 b(Then)22 b Fw(X)28 b FE(cannot)20 b(b)r(elong)208 1921 y(to)27 b Fu(cutset)p FE(\()p Fw(T)12 b FE(\),)27 b(whic)n(h)g(is)h(equal)f(to)g Fu(va)n(rs)q FE(\()p Fw(T)1564 1891 y Fj(l)1588 1921 y FE(\))19 b Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)1942 1891 y Fj(r)1978 1921 y FE(\))g Fv(\000)f Fu(acutset)o FE(\()p Fw(T)12 b FE(\).)37 b(The)27 b(other)g(direction)h(follo)n(ws)e (similarly)-7 b(.)55 2081 y(\(b\))43 b(Supp)r(ose)34 b Fw(X)40 b Fv(2)35 b Fu(context)o FE(\()p Fw(T)12 b FE(\).)57 b(Then)34 b Fw(X)40 b Fv(2)35 b Fu(acutset)o FE(\()p Fw(T)12 b FE(\))23 b Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))34 b(and,)i(hence,)g Fw(X)k Fv(2)34 b Fu(va)n(rs)p FE(\()p Fw(T)3273 2051 y Fj(p)3311 2081 y FE(\).)57 b(W)-7 b(e)35 b(ha)n(v)n(e)e(t)n(w)n(o)208 2181 y(cases.)307 2341 y Fv(\017)41 b Fw(X)30 b Fv(2)23 b Fu(acutset)o FE(\()p Fw(T)908 2310 y Fj(p)946 2341 y FE(\):)37 b(Then)28 b Fw(X)h Fv(2)24 b Fu(context)o FE(\()p Fw(T)1781 2310 y Fj(p)1819 2341 y FE(\).)307 2467 y Fv(\017)41 b Fw(X)30 b Fv(62)23 b Fu(acutset)o FE(\()p Fw(T)908 2437 y Fj(p)946 2467 y FE(\):)37 b(Then)28 b Fw(X)h Fv(2)24 b Fu(cutset)o FE(\()p Fw(T)1733 2437 y Fj(p)1771 2467 y FE(\))k(since)f Fw(X)j Fv(2)23 b Fu(acutset)p FE(\()p Fw(T)12 b FE(\).)208 2628 y(Therefore,)26 b Fw(X)j Fv(2)24 b Fu(context)o FE(\()p Fw(T)1133 2597 y Fj(p)1171 2628 y FE(\))k(or)f Fw(X)i Fv(2)23 b Fu(cutset)p FE(\()p Fw(T)1811 2597 y Fj(p)1849 2628 y FE(\).)65 2788 y(\(c\))42 b(Let)28 b Fw(T)418 2758 y Fj(s)481 2788 y FE(b)r(e)g(the)h(sibling)f (of)g Fw(T)40 b FE(and)28 b(supp)r(ose)g Fw(X)i Fv(2)25 b Fu(cutset)o FE(\()p Fw(T)2141 2758 y Fj(p)2179 2788 y FE(\).)39 b(Then)28 b Fw(X)j Fv(2)24 b Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))19 b Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)3252 2758 y Fj(s)3287 2788 y FE(\))29 b(b)n(y)e(de\014nition)i(of) 208 2887 y(a)e(cutset.)37 b(Therefore,)26 b Fw(X)k Fv(2)23 b Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\),)28 b Fw(X)h Fv(2)23 b Fu(acutset)p FE(\()p Fw(T)12 b FE(\))27 b(and,)g(hence,)h Fw(X)i Fv(2)23 b Fu(context)o FE(\()p Fw(T)12 b FE(\).)55 3047 y(\(d\))43 b(W)-7 b(e)31 b(ha)n(v)n(e)f Fu(cutset)p FE(\()p Fw(T)839 3059 y Fq(1)876 3047 y FE(\))f Fv(\022)g Fu(acutset)o FE(\()p Fw(T)1360 3059 y Fq(2)1397 3047 y FE(\))j(b)n(y)f(de\014nition)g(of)g Fu(acutset)p FE(.)47 b(W)-7 b(e)32 b(also)e(ha)n(v)n(e)g Fu(cutset)p FE(\()p Fw(T)3171 3059 y Fq(2)3208 3047 y FE(\))21 b Fv(\\)g Fu(acutset)o FE(\()p Fw(T)3666 3059 y Fq(2)3703 3047 y FE(\))30 b(=)e Fv(;)208 3147 y FE(b)n(y)f(de\014nition)h(of)f Fu(cutset)p FE(.)37 b(Hence,)28 b Fu(cutset)o FE(\()p Fw(T)1614 3159 y Fq(1)1651 3147 y FE(\))19 b Fv(\\)g Fu(cutset)o FE(\()p Fw(T)2065 3159 y Fq(2)2102 3147 y FE(\))24 b(=)e Fv(;)p FE(.)65 3307 y(\(e\))42 b(By)29 b(de\014nition)i(of)f(con)n(text,)g(w)n(e)g(ha)n(v)n(e)f Fu(context)p FE(\()p Fw(T)12 b FE(\))27 b Fv(\022)g Fu(cluster)p FE(\()p Fw(T)12 b FE(\).)45 b(By)29 b(\(b\),)j(w)n(e)e(ha)n(v)n(e)f Fu(context)o FE(\()p Fw(T)12 b FE(\))27 b Fv(\022)g Fu(cluster)q FE(\()p Fw(T)3807 3277 y Fj(p)3845 3307 y FE(\).)208 3407 y(Hence,)32 b Fu(context)p FE(\()p Fw(T)12 b FE(\))29 b Fv(\022)h Fu(cluster)q FE(\()p Fw(T)12 b FE(\))21 b Fv(\\)g Fu(cluster)q FE(\()p Fw(T)1759 3377 y Fj(p)1797 3407 y FE(\).)49 b(Supp)r(ose)32 b(that)g Fw(X)k Fv(2)30 b Fu(cluster)q FE(\()p Fw(T)12 b FE(\))21 b Fv(\\)g Fu(cluster)q FE(\()p Fw(T)3376 3377 y Fj(p)3414 3407 y FE(\).)50 b(Then)31 b Fw(X)37 b Fv(2)208 3506 y Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))23 b(since)h Fw(X)30 b Fv(2)23 b Fu(cluster)q FE(\()p Fw(T)12 b FE(\).)35 b(Since)25 b Fw(X)k Fv(2)23 b Fu(cluster)q FE(\()p Fw(T)1991 3476 y Fj(p)2029 3506 y FE(\),)i(w)n(e)f(ha)n(v)n(e)f(t)n(w)n(o)g(cases.)35 b(Case)23 b(1:)35 b Fw(X)29 b Fv(2)24 b Fu(cutset)o FE(\()p Fw(T)3582 3476 y Fj(p)3620 3506 y FE(\).)36 b(Then)208 3606 y Fw(X)29 b Fv(2)23 b Fu(context)p FE(\()p Fw(T)12 b FE(\))23 b(b)n(y)h(\(c\).)36 b(Case)23 b(2:)34 b Fw(X)c Fv(62)23 b Fu(cutset)p FE(\()p Fw(T)1834 3576 y Fj(p)1871 3606 y FE(\).)36 b(Then)24 b Fw(X)30 b Fv(2)23 b Fu(context)p FE(\()p Fw(T)2702 3576 y Fj(p)2739 3606 y FE(\))h(b)n(y)g(\(a\);)h (hence,)g Fw(X)k Fv(2)24 b Fu(acutset)o FE(\()p Fw(T)3830 3576 y Fj(p)3868 3606 y FE(\))208 3706 y(and)j Fw(X)i Fv(2)24 b Fu(va)n(rs)p FE(\()p Fw(T)775 3675 y Fj(p)813 3706 y FE(\).)37 b(Therefore,)26 b Fw(X)k Fv(2)23 b Fu(acutset)o FE(\()p Fw(T)12 b FE(\))28 b(and)f Fw(X)i Fv(2)24 b Fu(context)o FE(\()p Fw(T)12 b FE(\).)p 2652 3681 48 4 v 2652 3730 4 50 v 2696 3730 V 2652 3733 48 4 v 0 3873 a Ft(Lemma)30 b(2)41 b Fx(L)l(et)26 b Fu(va)n(rs)704 3843 y Fp(")742 3873 y FE(\()p Fw(T)12 b FE(\))27 b Fx(denote)g Fv([)1211 3885 y Fj(T)1259 3869 y Fa(0)1286 3873 y Fu(va)n(rs)p FE(\()p Fw(T)1515 3843 y Fp(0)1538 3873 y FE(\))p Fx(,)h(wher)l(e)f Fw(T)1915 3843 y Fp(0)1964 3873 y Fx(is)h(a)f(le)l(af)h(c)l(onne)l(cte) l(d)e(to)h(no)l(de)g Fw(T)38 b Fx(thr)l(ough)27 b(its)g(p)l(ar)l(ent.) 37 b(Then)471 4041 y Fu(cutset)o FE(\()p Fw(T)12 b FE(\))83 b(=)f Fu(va)n(rs)p FE(\()p Fw(T)1263 4007 y Fj(l)1288 4041 y FE(\))19 b Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)1642 4007 y Fj(r)1678 4041 y FE(\))g Fv(\000)f Fu(va)n(rs)1948 4007 y Fp(")1986 4041 y FE(\()p Fw(T)12 b FE(\))423 4166 y Fu(context)o FE(\()p Fw(T)g FE(\))83 b(=)f Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))19 b Fv(\\)f Fu(va)n(rs)1523 4131 y Fp(")1562 4166 y FE(\()p Fw(T)12 b FE(\))451 4290 y Fu(cluster)q FE(\()p Fw(T)g FE(\))83 b(=)f(\()p Fu(va)n(rs)q FE(\()p Fw(T)1296 4256 y Fj(l)1321 4290 y FE(\))18 b Fv(\\)h Fu(va)n(rs)p FE(\()p Fw(T)1674 4256 y Fj(r)1710 4290 y FE(\)\))g Fv([)g FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)2128 4256 y Fj(l)2153 4290 y FE(\))g Fv(\\)g Fu(va)n(rs)2414 4256 y Fp(")2452 4290 y FE(\()p Fw(T)12 b FE(\)\))18 b Fv([)h FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)2962 4256 y Fj(r)2999 4290 y FE(\))f Fv(\\)h Fu(va)n(rs)3259 4256 y Fp(")3297 4290 y FE(\()p Fw(T)12 b FE(\)\))p Fw(:)0 4520 y Fb(Pro)s(of)37 b(of)h(Lemma)f(2)0 4673 y FE(If)d Fw(X)39 b Fv(2)33 b Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\),)35 b(then)e Fw(X)39 b Fv(2)33 b Fu(va)n(rs)1131 4643 y Fp(")1169 4673 y FE(\()p Fw(T)12 b FE(\))33 b(i\013)h Fw(X)39 b Fv(2)33 b Fu(acutset)o FE(\()p Fw(T)12 b FE(\).)54 b(This)33 b(immediately)h(leads)f(to)g Fu(cutset)p FE(\()p Fw(T)12 b FE(\))32 b(=)g Fu(va)n(rs)p FE(\()p Fw(T)3765 4643 y Fj(l)3790 4673 y FE(\))23 b Fv(\\)0 4773 y Fu(va)n(rs)p FE(\()p Fw(T)229 4743 y Fj(r)265 4773 y FE(\))c Fv(\000)f Fu(va)n(rs)535 4743 y Fp(")573 4773 y FE(\()p Fw(T)12 b FE(\))27 b(and)h Fu(context)o FE(\()p Fw(T)12 b FE(\))23 b(=)g Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)h Fu(va)n(rs)1868 4743 y Fp(")1906 4773 y FE(\()p Fw(T)12 b FE(\).)125 4872 y(Supp)r(ose)27 b(that)640 5040 y Fw(X)j Fv(2)23 b FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)1078 5006 y Fj(l)1103 5040 y FE(\))c Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)1457 5006 y Fj(r)1493 5040 y FE(\)\))g Fv([)g FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)1911 5006 y Fj(l)1936 5040 y FE(\))f Fv(\\)h Fu(va)n(rs)2196 5006 y Fp(")2235 5040 y FE(\()p Fw(T)12 b FE(\)\))18 b Fv([)h FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)2745 5006 y Fj(r)2781 5040 y FE(\))g Fv(\\)g Fu(va)n(rs)3042 5006 y Fp(")3080 5040 y FE(\()p Fw(T)12 b FE(\)\))p Fw(:)0 5208 y FE(If)28 b Fw(X)i Fv(2)24 b FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)522 5178 y Fj(l)547 5208 y FE(\))19 b Fv(\\)g Fu(va)n(rs)808 5178 y Fp(")846 5208 y FE(\()p Fw(T)12 b FE(\)\))19 b Fv([)g FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)1357 5178 y Fj(r)1393 5208 y FE(\))g Fv(\\)g Fu(va)n(rs)1654 5178 y Fp(")1693 5208 y FE(\()p Fw(T)12 b FE(\)\),)28 b(then)g Fw(X)i Fv(2)24 b Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)h Fu(va)n(rs)2757 5178 y Fp(")2795 5208 y FE(\()p Fw(T)12 b FE(\))24 b(=)f Fu(context)o FE(\()p Fw(T)12 b FE(\))23 b Fv(\022)g Fu(cluster)q FE(\()p Fw(T)12 b FE(\).)0 5308 y(If)33 b Fw(X)38 b Fv(62)32 b FE(\()p Fu(va)n(rs)q FE(\()p Fw(T)544 5277 y Fj(l)569 5308 y FE(\))22 b Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)929 5277 y Fj(r)965 5308 y FE(\)\))h Fv([)f FE(\()p Fu(va)n(rs)p FE(\()p Fw(T)1390 5277 y Fj(r)1426 5308 y FE(\))h Fv(\\)f Fu(va)n(rs)1694 5277 y Fp(")1732 5308 y FE(\()p Fw(T)12 b FE(\)\))33 b(and)g Fw(X)38 b Fv(2)32 b Fu(va)n(rs)p FE(\()p Fw(T)2512 5277 y Fj(l)2537 5308 y FE(\))22 b Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)2897 5277 y Fj(r)2933 5308 y FE(\),)35 b(then)e Fw(X)38 b Fv(62)32 b Fu(va)n(rs)3547 5277 y Fp(")3586 5308 y FE(\()p Fw(T)12 b FE(\))32 b(and,)0 5407 y(hence,)c Fw(X)h Fv(2)23 b Fu(va)n(rs)q FE(\()p Fw(T)660 5377 y Fj(l)684 5407 y FE(\))c Fv(\\)g Fu(va)n(rs)p FE(\()p Fw(T)1038 5377 y Fj(r)1074 5407 y FE(\))g Fv(\000)f Fu(va)n(rs)1344 5377 y Fp(")1382 5407 y FE(\()p Fw(T)12 b FE(\))23 b(=)f Fu(cutset)p FE(\()p Fw(T)12 b FE(\))22 b Fv(\022)h Fu(cluster)q FE(\()p Fw(T)12 b FE(\).)1908 5656 y(22)p eop %%Page: 23 23 23 22 bop 651 2250 a @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 3118 @rwi @setspecial %%BeginDocument: widths20.ps %!PS-Adobe-2.0 EPSF-2.0 %%Title: c:/windows/desktop/rc/results/n10020/widths.ps %%Creator: gnuplot 3.7 patchlevel 0 %%CreationDate: Thu Jul 22 11:36:43 1999 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -53 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Latex) findfont 160 scalefont setfont 1.000 UL LTb 624 480 M 63 0 V 6241 0 R -63 0 V 528 480 M (0) Rshow 624 933 M 63 0 V 6241 0 R -63 0 V 528 933 M (2) Rshow 624 1387 M 63 0 V 6241 0 R -63 0 V -6337 0 R (4) Rshow 624 1840 M 63 0 V 6241 0 R -63 0 V -6337 0 R (6) Rshow 624 2293 M 63 0 V 6241 0 R -63 0 V -6337 0 R (8) Rshow 624 2747 M 63 0 V 6241 0 R -63 0 V -6337 0 R (10) Rshow 624 3200 M 63 0 V 6241 0 R -63 0 V -6337 0 R (12) Rshow 624 3653 M 63 0 V 6241 0 R -63 0 V -6337 0 R (14) Rshow 624 4107 M 63 0 V 6241 0 R -63 0 V -6337 0 R (16) Rshow 624 4560 M 63 0 V 6241 0 R -63 0 V -6337 0 R (18) Rshow 624 480 M 0 63 V 0 4017 R 0 -63 V 624 320 M (0) Cshow 1254 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (100) Cshow 1885 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (200) Cshow 2515 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (300) Cshow 3146 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (400) Cshow 3776 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (500) Cshow 4406 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (600) Cshow 5037 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (700) Cshow 5667 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (800) Cshow 6298 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (900) Cshow 6928 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (1000) Cshow 1.000 UL LTb 624 480 M 6304 0 V 0 4080 V -6304 0 V 624 480 L 160 2520 M currentpoint gsave translate 90 rotate 0 0 M (Width) Cshow grestore 3776 80 M (Samples) Cshow 3776 4800 M (Distribution of 1000 Random Networks --- Set A) Cshow 1.000 UP 1.000 UL LT0 624 1613 Pls 630 2520 Pls 637 3880 Pls 643 2067 Pls 649 3880 Pls 656 2747 Pls 662 2973 Pls 668 2293 Pls 674 2520 Pls 681 3200 Pls 687 1613 Pls 693 1840 Pls 700 3200 Pls 706 2973 Pls 712 2067 Pls 719 2520 Pls 725 3653 Pls 731 3653 Pls 737 2293 Pls 744 1613 Pls 750 3880 Pls 756 2520 Pls 763 3427 Pls 769 933 Pls 775 1387 Pls 782 2293 Pls 788 3427 Pls 794 1613 Pls 801 2293 Pls 807 1840 Pls 813 3200 Pls 819 2067 Pls 826 3653 Pls 832 3653 Pls 838 2067 Pls 845 2973 Pls 851 1387 Pls 857 1840 Pls 864 1613 Pls 870 3200 Pls 876 2293 Pls 882 1387 Pls 889 2067 Pls 895 933 Pls 901 2067 Pls 908 3200 Pls 914 3200 Pls 920 1387 Pls 927 2293 Pls 933 933 Pls 939 3653 Pls 946 2067 Pls 952 2520 Pls 958 2293 Pls 964 2293 Pls 971 3427 Pls 977 2520 Pls 983 1840 Pls 990 3200 Pls 996 2293 Pls 1002 3653 Pls 1009 2067 Pls 1015 3427 Pls 1021 2520 Pls 1027 2973 Pls 1034 3880 Pls 1040 3653 Pls 1046 1387 Pls 1053 2520 Pls 1059 2067 Pls 1065 2973 Pls 1072 3653 Pls 1078 2973 Pls 1084 4107 Pls 1090 2973 Pls 1097 3653 Pls 1103 1160 Pls 1109 933 Pls 1116 1840 Pls 1122 1613 Pls 1128 3427 Pls 1135 1387 Pls 1141 1387 Pls 1147 2747 Pls 1154 2747 Pls 1160 3427 Pls 1166 1840 Pls 1172 2973 Pls 1179 933 Pls 1185 1840 Pls 1191 2520 Pls 1198 2747 Pls 1204 2973 Pls 1210 2520 Pls 1217 2747 Pls 1223 2067 Pls 1229 2520 Pls 1235 2293 Pls 1242 1613 Pls 1248 2747 Pls 1254 2293 Pls 1261 2520 Pls 1267 1840 Pls 1273 3200 Pls 1280 933 Pls 1286 2747 Pls 1292 3653 Pls 1299 1160 Pls 1305 2520 Pls 1311 2067 Pls 1317 3200 Pls 1324 2973 Pls 1330 2293 Pls 1336 1160 Pls 1343 3427 Pls 1349 3427 Pls 1355 2293 Pls 1362 2520 Pls 1368 1387 Pls 1374 2747 Pls 1380 2747 Pls 1387 1840 Pls 1393 1387 Pls 1399 2747 Pls 1406 1840 Pls 1412 2293 Pls 1418 3653 Pls 1425 4107 Pls 1431 1160 Pls 1437 2747 Pls 1444 2520 Pls 1450 2293 Pls 1456 1613 Pls 1462 2520 Pls 1469 2973 Pls 1475 1160 Pls 1481 3427 Pls 1488 4107 Pls 1494 1613 Pls 1500 1613 Pls 1507 2747 Pls 1513 1387 Pls 1519 1840 Pls 1525 2973 Pls 1532 2067 Pls 1538 933 Pls 1544 1613 Pls 1551 2747 Pls 1557 2067 Pls 1563 1840 Pls 1570 3427 Pls 1576 3653 Pls 1582 933 Pls 1589 2067 Pls 1595 2067 Pls 1601 2747 Pls 1607 3880 Pls 1614 1387 Pls 1620 2747 Pls 1626 2520 Pls 1633 2520 Pls 1639 3200 Pls 1645 1160 Pls 1652 1387 Pls 1658 1613 Pls 1664 3200 Pls 1670 2293 Pls 1677 3200 Pls 1683 2067 Pls 1689 3200 Pls 1696 3427 Pls 1702 2067 Pls 1708 933 Pls 1715 3200 Pls 1721 1613 Pls 1727 933 Pls 1734 2747 Pls 1740 3200 Pls 1746 2293 Pls 1752 1613 Pls 1759 2067 Pls 1765 2520 Pls 1771 933 Pls 1778 3653 Pls 1784 3427 Pls 1790 2973 Pls 1797 3653 Pls 1803 2293 Pls 1809 4333 Pls 1815 3427 Pls 1822 2067 Pls 1828 2973 Pls 1834 2293 Pls 1841 2747 Pls 1847 2973 Pls 1853 2520 Pls 1860 1160 Pls 1866 3427 Pls 1872 1387 Pls 1878 1387 Pls 1885 1613 Pls 1891 2520 Pls 1897 2067 Pls 1904 2520 Pls 1910 2747 Pls 1916 2973 Pls 1923 2747 Pls 1929 3427 Pls 1935 3653 Pls 1942 2067 Pls 1948 1840 Pls 1954 3427 Pls 1960 2067 Pls 1967 2973 Pls 1973 2067 Pls 1979 2747 Pls 1986 2520 Pls 1992 2973 Pls 1998 2067 Pls 2005 3427 Pls 2011 2067 Pls 2017 2293 Pls 2023 1840 Pls 2030 1160 Pls 2036 3200 Pls 2042 933 Pls 2049 2747 Pls 2055 3200 Pls 2061 1840 Pls 2068 2747 Pls 2074 3653 Pls 2080 3427 Pls 2087 1387 Pls 2093 1840 Pls 2099 3427 Pls 2105 3653 Pls 2112 2520 Pls 2118 1840 Pls 2124 2973 Pls 2131 3880 Pls 2137 2520 Pls 2143 2973 Pls 2150 2067 Pls 2156 2973 Pls 2162 2293 Pls 2168 3427 Pls 2175 1387 Pls 2181 2067 Pls 2187 933 Pls 2194 2973 Pls 2200 1840 Pls 2206 2067 Pls 2213 3880 Pls 2219 3427 Pls 2225 933 Pls 2232 2293 Pls 2238 1387 Pls 2244 3653 Pls 2250 2973 Pls 2257 3200 Pls 2263 2067 Pls 2269 2747 Pls 2276 3653 Pls 2282 3200 Pls 2288 2747 Pls 2295 3653 Pls 2301 1387 Pls 2307 933 Pls 2313 3200 Pls 2320 2973 Pls 2326 2520 Pls 2332 3200 Pls 2339 1387 Pls 2345 2293 Pls 2351 2520 Pls 2358 2520 Pls 2364 3880 Pls 2370 1160 Pls 2377 2973 Pls 2383 3653 Pls 2389 933 Pls 2395 2293 Pls 2402 2973 Pls 2408 2293 Pls 2414 933 Pls 2421 2747 Pls 2427 3880 Pls 2433 2520 Pls 2440 1840 Pls 2446 2973 Pls 2452 1160 Pls 2458 2067 Pls 2465 2973 Pls 2471 1613 Pls 2477 3427 Pls 2484 1840 Pls 2490 2747 Pls 2496 1613 Pls 2503 2747 Pls 2509 2973 Pls 2515 3427 Pls 2522 2067 Pls 2528 2973 Pls 2534 3880 Pls 2540 2520 Pls 2547 2067 Pls 2553 1160 Pls 2559 1840 Pls 2566 1840 Pls 2572 2293 Pls 2578 1387 Pls 2585 1613 Pls 2591 3653 Pls 2597 2067 Pls 2603 1160 Pls 2610 4107 Pls 2616 2067 Pls 2622 3653 Pls 2629 933 Pls 2635 2747 Pls 2641 2973 Pls 2648 3880 Pls 2654 1840 Pls 2660 933 Pls 2666 1387 Pls 2673 3200 Pls 2679 933 Pls 2685 1387 Pls 2692 2747 Pls 2698 3200 Pls 2704 2747 Pls 2711 2293 Pls 2717 1840 Pls 2723 3200 Pls 2730 3427 Pls 2736 1160 Pls 2742 1387 Pls 2748 3880 Pls 2755 3200 Pls 2761 3200 Pls 2767 3653 Pls 2774 1840 Pls 2780 3427 Pls 2786 2973 Pls 2793 2293 Pls 2799 2293 Pls 2805 2747 Pls 2811 2067 Pls 2818 2067 Pls 2824 2293 Pls 2830 1840 Pls 2837 3200 Pls 2843 2520 Pls 2849 2067 Pls 2856 2067 Pls 2862 2520 Pls 2868 2067 Pls 2875 2747 Pls 2881 2747 Pls 2887 2067 Pls 2893 3653 Pls 2900 2520 Pls 2906 3427 Pls 2912 1160 Pls 2919 2973 Pls 2925 933 Pls 2931 1160 Pls 2938 2973 Pls 2944 933 Pls 2950 2293 Pls 2956 1613 Pls 2963 2973 Pls 2969 1387 Pls 2975 2520 Pls 2982 3427 Pls 2988 2520 Pls 2994 2520 Pls 3001 1160 Pls 3007 2973 Pls 3013 2067 Pls 3020 3200 Pls 3026 2973 Pls 3032 1840 Pls 3038 2973 Pls 3045 3200 Pls 3051 2520 Pls 3057 933 Pls 3064 1387 Pls 3070 3200 Pls 3076 1613 Pls 3083 2520 Pls 3089 4107 Pls 3095 2293 Pls 3101 1160 Pls 3108 2293 Pls 3114 2747 Pls 3120 3427 Pls 3127 1840 Pls 3133 2973 Pls 3139 1613 Pls 3146 1840 Pls 3152 1840 Pls 3158 2293 Pls 3165 2520 Pls 3171 3200 Pls 3177 3427 Pls 3183 3200 Pls 3190 1613 Pls 3196 2520 Pls 3202 1387 Pls 3209 3200 Pls 3215 2747 Pls 3221 2293 Pls 3228 1613 Pls 3234 1387 Pls 3240 2973 Pls 3246 3427 Pls 3253 2293 Pls 3259 3427 Pls 3265 933 Pls 3272 2067 Pls 3278 2067 Pls 3284 3880 Pls 3291 933 Pls 3297 1160 Pls 3303 1840 Pls 3310 1613 Pls 3316 3427 Pls 3322 2067 Pls 3328 3880 Pls 3335 1387 Pls 3341 2067 Pls 3347 1840 Pls 3354 1613 Pls 3360 3427 Pls 3366 2520 Pls 3373 1840 Pls 3379 2747 Pls 3385 2973 Pls 3391 2293 Pls 3398 2747 Pls 3404 1387 Pls 3410 1160 Pls 3417 2973 Pls 3423 2520 Pls 3429 2973 Pls 3436 3653 Pls 3442 3427 Pls 3448 4107 Pls 3454 2293 Pls 3461 2067 Pls 3467 2973 Pls 3473 1387 Pls 3480 2067 Pls 3486 2293 Pls 3492 2520 Pls 3499 1160 Pls 3505 2293 Pls 3511 2747 Pls 3518 3427 Pls 3524 3880 Pls 3530 3200 Pls 3536 2973 Pls 3543 2747 Pls 3549 1613 Pls 3555 3653 Pls 3562 4107 Pls 3568 2067 Pls 3574 1387 Pls 3581 2520 Pls 3587 933 Pls 3593 2520 Pls 3599 2293 Pls 3606 2067 Pls 3612 2747 Pls 3618 933 Pls 3625 1160 Pls 3631 3200 Pls 3637 3653 Pls 3644 3200 Pls 3650 2520 Pls 3656 2293 Pls 3663 1160 Pls 3669 3880 Pls 3675 3880 Pls 3681 2067 Pls 3688 1840 Pls 3694 3200 Pls 3700 1160 Pls 3707 1840 Pls 3713 2747 Pls 3719 2293 Pls 3726 3427 Pls 3732 3427 Pls 3738 3200 Pls 3744 3200 Pls 3751 933 Pls 3757 2067 Pls 3763 3880 Pls 3770 1160 Pls 3776 1387 Pls 3782 1840 Pls 3789 2973 Pls 3795 2520 Pls 3801 2747 Pls 3808 2067 Pls 3814 2747 Pls 3820 3653 Pls 3826 1840 Pls 3833 2747 Pls 3839 2973 Pls 3845 3427 Pls 3852 2293 Pls 3858 2293 Pls 3864 1613 Pls 3871 2747 Pls 3877 3427 Pls 3883 1387 Pls 3889 2067 Pls 3896 4107 Pls 3902 2747 Pls 3908 2973 Pls 3915 2747 Pls 3921 3427 Pls 3927 2973 Pls 3934 3427 Pls 3940 3427 Pls 3946 2293 Pls 3953 3427 Pls 3959 2293 Pls 3965 1840 Pls 3971 2067 Pls 3978 933 Pls 3984 2293 Pls 3990 2067 Pls 3997 1160 Pls 4003 1840 Pls 4009 1613 Pls 4016 3200 Pls 4022 3880 Pls 4028 2973 Pls 4034 2747 Pls 4041 3653 Pls 4047 933 Pls 4053 933 Pls 4060 3427 Pls 4066 2520 Pls 4072 1840 Pls 4079 2067 Pls 4085 1160 Pls 4091 3653 Pls 4098 2747 Pls 4104 3653 Pls 4110 3880 Pls 4116 2520 Pls 4123 3200 Pls 4129 4107 Pls 4135 3880 Pls 4142 2520 Pls 4148 1613 Pls 4154 3200 Pls 4161 3427 Pls 4167 2747 Pls 4173 2293 Pls 4179 2293 Pls 4186 2067 Pls 4192 1840 Pls 4198 1160 Pls 4205 1387 Pls 4211 2520 Pls 4217 1840 Pls 4224 2520 Pls 4230 3200 Pls 4236 3427 Pls 4242 1613 Pls 4249 3200 Pls 4255 933 Pls 4261 2520 Pls 4268 3427 Pls 4274 3653 Pls 4280 4107 Pls 4287 2293 Pls 4293 2067 Pls 4299 2973 Pls 4306 4333 Pls 4312 2293 Pls 4318 2067 Pls 4324 1840 Pls 4331 2973 Pls 4337 2067 Pls 4343 3880 Pls 4350 1613 Pls 4356 1840 Pls 4362 4333 Pls 4369 2973 Pls 4375 2973 Pls 4381 2520 Pls 4387 2747 Pls 4394 933 Pls 4400 3427 Pls 4406 1840 Pls 4413 2747 Pls 4419 3200 Pls 4425 2293 Pls 4432 1840 Pls 4438 3427 Pls 4444 933 Pls 4451 2520 Pls 4457 2747 Pls 4463 2973 Pls 4469 2067 Pls 4476 3200 Pls 4482 3427 Pls 4488 2747 Pls 4495 2973 Pls 4501 2973 Pls 4507 3653 Pls 4514 3427 Pls 4520 1840 Pls 4526 2747 Pls 4532 2973 Pls 4539 933 Pls 4545 3427 Pls 4551 2747 Pls 4558 933 Pls 4564 3200 Pls 4570 3200 Pls 4577 2520 Pls 4583 3200 Pls 4589 1613 Pls 4596 2520 Pls 4602 2520 Pls 4608 2067 Pls 4614 2520 Pls 4621 2520 Pls 4627 1840 Pls 4633 3427 Pls 4640 3653 Pls 4646 933 Pls 4652 3880 Pls 4659 2067 Pls 4665 2293 Pls 4671 3427 Pls 4677 2973 Pls 4684 2520 Pls 4690 2973 Pls 4696 3653 Pls 4703 2973 Pls 4709 2747 Pls 4715 2747 Pls 4722 3427 Pls 4728 3427 Pls 4734 2067 Pls 4741 1160 Pls 4747 2973 Pls 4753 3880 Pls 4759 1840 Pls 4766 1160 Pls 4772 2293 Pls 4778 933 Pls 4785 3200 Pls 4791 1387 Pls 4797 2973 Pls 4804 2293 Pls 4810 2293 Pls 4816 1160 Pls 4822 2067 Pls 4829 3200 Pls 4835 3653 Pls 4841 2293 Pls 4848 2747 Pls 4854 2293 Pls 4860 2293 Pls 4867 2973 Pls 4873 2973 Pls 4879 2747 Pls 4886 933 Pls 4892 1840 Pls 4898 2747 Pls 4904 3653 Pls 4911 1160 Pls 4917 1387 Pls 4923 1387 Pls 4930 1840 Pls 4936 933 Pls 4942 3880 Pls 4949 2973 Pls 4955 2293 Pls 4961 1160 Pls 4967 2520 Pls 4974 1160 Pls 4980 3427 Pls 4986 2520 Pls 4993 2520 Pls 4999 3880 Pls 5005 2973 Pls 5012 1840 Pls 5018 2293 Pls 5024 933 Pls 5030 2973 Pls 5037 3653 Pls 5043 2747 Pls 5049 1613 Pls 5056 4107 Pls 5062 2520 Pls 5068 2747 Pls 5075 3653 Pls 5081 3653 Pls 5087 2520 Pls 5094 3200 Pls 5100 933 Pls 5106 1160 Pls 5112 3653 Pls 5119 3880 Pls 5125 1840 Pls 5131 2067 Pls 5138 2520 Pls 5144 3200 Pls 5150 2973 Pls 5157 2520 Pls 5163 2973 Pls 5169 3653 Pls 5175 2067 Pls 5182 3653 Pls 5188 2520 Pls 5194 2973 Pls 5201 2293 Pls 5207 3427 Pls 5213 3200 Pls 5220 1840 Pls 5226 3880 Pls 5232 2747 Pls 5239 2747 Pls 5245 2293 Pls 5251 1387 Pls 5257 1840 Pls 5264 933 Pls 5270 2973 Pls 5276 1387 Pls 5283 2973 Pls 5289 1160 Pls 5295 1840 Pls 5302 3200 Pls 5308 1160 Pls 5314 2520 Pls 5320 3200 Pls 5327 3200 Pls 5333 3200 Pls 5339 3427 Pls 5346 1160 Pls 5352 2520 Pls 5358 2067 Pls 5365 2067 Pls 5371 2973 Pls 5377 2520 Pls 5384 2747 Pls 5390 2067 Pls 5396 3200 Pls 5402 1613 Pls 5409 2520 Pls 5415 3653 Pls 5421 2293 Pls 5428 2067 Pls 5434 2067 Pls 5440 1840 Pls 5447 4107 Pls 5453 2973 Pls 5459 3200 Pls 5465 1840 Pls 5472 4107 Pls 5478 1160 Pls 5484 3200 Pls 5491 2520 Pls 5497 1840 Pls 5503 1613 Pls 5510 2747 Pls 5516 2747 Pls 5522 1840 Pls 5529 3427 Pls 5535 2520 Pls 5541 2520 Pls 5547 1840 Pls 5554 2067 Pls 5560 933 Pls 5566 2293 Pls 5573 1387 Pls 5579 2520 Pls 5585 1840 Pls 5592 2973 Pls 5598 2293 Pls 5604 3427 Pls 5610 3880 Pls 5617 1613 Pls 5623 2067 Pls 5629 2293 Pls 5636 2293 Pls 5642 3653 Pls 5648 2067 Pls 5655 2293 Pls 5661 3200 Pls 5667 1840 Pls 5674 3427 Pls 5680 3880 Pls 5686 3653 Pls 5692 2293 Pls 5699 3427 Pls 5705 2067 Pls 5711 1840 Pls 5718 2067 Pls 5724 2293 Pls 5730 1840 Pls 5737 1387 Pls 5743 3427 Pls 5749 2747 Pls 5755 1160 Pls 5762 2747 Pls 5768 933 Pls 5774 933 Pls 5781 4107 Pls 5787 2747 Pls 5793 1160 Pls 5800 2067 Pls 5806 1840 Pls 5812 2067 Pls 5818 3880 Pls 5825 3880 Pls 5831 2747 Pls 5837 3200 Pls 5844 2520 Pls 5850 3427 Pls 5856 3880 Pls 5863 3880 Pls 5869 1160 Pls 5875 2747 Pls 5882 1160 Pls 5888 2067 Pls 5894 2520 Pls 5900 2520 Pls 5907 2067 Pls 5913 3200 Pls 5919 3200 Pls 5926 1840 Pls 5932 2747 Pls 5938 3200 Pls 5945 2067 Pls 5951 2293 Pls 5957 1840 Pls 5963 3200 Pls 5970 2520 Pls 5976 2747 Pls 5982 1840 Pls 5989 1840 Pls 5995 1160 Pls 6001 2973 Pls 6008 933 Pls 6014 2293 Pls 6020 3427 Pls 6027 933 Pls 6033 2293 Pls 6039 3200 Pls 6045 3200 Pls 6052 2973 Pls 6058 933 Pls 6064 2067 Pls 6071 1840 Pls 6077 2293 Pls 6083 3427 Pls 6090 3427 Pls 6096 3880 Pls 6102 2747 Pls 6108 2520 Pls 6115 2520 Pls 6121 2067 Pls 6127 933 Pls 6134 2973 Pls 6140 2520 Pls 6146 933 Pls 6153 1840 Pls 6159 3427 Pls 6165 2747 Pls 6172 3427 Pls 6178 2293 Pls 6184 2520 Pls 6190 2293 Pls 6197 2973 Pls 6203 2973 Pls 6209 2747 Pls 6216 3653 Pls 6222 2293 Pls 6228 2067 Pls 6235 2293 Pls 6241 1840 Pls 6247 3200 Pls 6253 3653 Pls 6260 1840 Pls 6266 1613 Pls 6272 2747 Pls 6279 2520 Pls 6285 2520 Pls 6291 2067 Pls 6298 2747 Pls 6304 2973 Pls 6310 2067 Pls 6317 2747 Pls 6323 3653 Pls 6329 1387 Pls 6335 4107 Pls 6342 2067 Pls 6348 1840 Pls 6354 2293 Pls 6361 3200 Pls 6367 3200 Pls 6373 2973 Pls 6380 1840 Pls 6386 3200 Pls 6392 2520 Pls 6398 933 Pls 6405 1160 Pls 6411 2067 Pls 6417 2973 Pls 6424 3427 Pls 6430 2067 Pls 6436 2973 Pls 6443 2747 Pls 6449 1840 Pls 6455 3427 Pls 6462 2293 Pls 6468 2520 Pls 6474 2293 Pls 6480 2067 Pls 6487 1387 Pls 6493 2293 Pls 6499 933 Pls 6506 2067 Pls 6512 3653 Pls 6518 933 Pls 6525 2973 Pls 6531 933 Pls 6537 2520 Pls 6543 1840 Pls 6550 1840 Pls 6556 2747 Pls 6562 1387 Pls 6569 1840 Pls 6575 3427 Pls 6581 1840 Pls 6588 3427 Pls 6594 3427 Pls 6600 2520 Pls 6606 1387 Pls 6613 3427 Pls 6619 3200 Pls 6625 1840 Pls 6632 1387 Pls 6638 3880 Pls 6644 3200 Pls 6651 933 Pls 6657 2293 Pls 6663 1840 Pls 6670 2747 Pls 6676 1840 Pls 6682 3427 Pls 6688 933 Pls 6695 2973 Pls 6701 3880 Pls 6707 2747 Pls 6714 1840 Pls 6720 2067 Pls 6726 2973 Pls 6733 3200 Pls 6739 2293 Pls 6745 2520 Pls 6751 933 Pls 6758 2747 Pls 6764 1160 Pls 6770 1840 Pls 6777 3880 Pls 6783 2973 Pls 6789 933 Pls 6796 933 Pls 6802 2520 Pls 6808 1387 Pls 6815 2747 Pls 6821 3200 Pls 6827 2747 Pls 6833 2293 Pls 6840 1840 Pls 6846 3427 Pls 6852 2293 Pls 6859 2973 Pls 6865 2067 Pls 6871 2747 Pls 6878 1613 Pls 6884 2293 Pls 6890 2293 Pls 6896 2973 Pls 6903 2520 Pls 6909 2520 Pls 6915 2293 Pls 6922 933 Pls stroke grestore end showpage %%Trailer %%DocumentFonts: Latex %%EndDocument @endspecial 1607 2613 a FE(Un)n(balanced)27 b(Dtrees)p 752 2646 2396 4 v 750 2745 4 100 v 802 2716 a(P)n(arameter)p 2129 2745 V 2146 2745 V 1015 w(Av)n(e)p 2393 2745 V 106 w(Std)p 2640 2745 V 123 w(Min)p 2885 2745 V 100 w(Max)p 3146 2745 V 752 2749 2396 4 v 750 2848 4 100 v 802 2819 a(Width)p 2129 2848 V 2146 2848 V 1163 w(8.8)p 2393 2848 V 140 w(3.7)p 2640 2848 V 140 w(2.0)p 2885 2848 V 138 w(17.0)p 3146 2848 V 752 2852 2396 4 v 750 2951 4 100 v 802 2921 a(Cutset)h(Width)p 2129 2951 V 2146 2951 V 895 w(5.2)p 2393 2951 V 140 w(2.2)p 2640 2951 V 140 w(2.0)p 2885 2951 V 138 w(13.0)p 3146 2951 V 752 2955 2396 4 v 750 3054 4 100 v 802 3024 a(Con)n(text)f(Width)p 2129 3054 V 2146 3054 V 845 w(9.0)p 2393 3054 V 140 w(3.2)p 2640 3054 V 140 w(2.0)p 2885 3054 V 138 w(16.0)p 3146 3054 V 752 3058 2396 4 v 750 3157 4 100 v 802 3127 a(A-Cutset)h(Width)p 2129 3157 V 2146 3157 V 805 w(51.8)p 2393 3157 V 98 w(15.4)p 2640 3157 V 98 w(7.0)p 2885 3157 V 138 w(93.0)p 3146 3157 V 752 3161 2396 4 v 1653 3330 a(Balanced)f(Dtrees)p 752 3363 V 750 3463 4 100 v 802 3433 a(P)n(arameter)p 2129 3463 V 2146 3463 V 1015 w(Av)n(e)p 2393 3463 V 106 w(Std)p 2640 3463 V 123 w(Min)p 2885 3463 V 100 w(Max)p 3146 3463 V 752 3466 2396 4 v 750 3566 4 100 v 802 3536 a(Width)p 2129 3566 V 2146 3566 V 1163 w(17.5)p 2393 3566 V 98 w(6.6)p 2640 3566 V 140 w(3.0)p 2885 3566 V 138 w(34.0)p 3146 3566 V 752 3569 2396 4 v 750 3669 4 100 v 802 3639 a(Cutset)h(Width)p 2129 3669 V 2146 3669 V 895 w(7.5)p 2393 3669 V 140 w(2.6)p 2640 3669 V 140 w(2.0)p 2885 3669 V 138 w(15.0)p 3146 3669 V 752 3672 2396 4 v 750 3772 4 100 v 802 3742 a(Con)n(text)f(Width)p 2129 3772 V 2146 3772 V 845 w(14.5)p 2393 3772 V 98 w(5.4)p 2640 3772 V 140 w(3.0)p 2885 3772 V 138 w(27.0)p 3146 3772 V 752 3775 2396 4 v 750 3875 4 100 v 802 3845 a(A-Cutset)h(Width)p 2129 3875 V 2146 3875 V 805 w(28.4)p 2393 3875 V 98 w(8.8)p 2640 3875 V 140 w(5.0)p 2885 3875 V 138 w(50.0)p 3146 3875 V 752 3878 2396 4 v 1410 4047 a(Balanced)f(/)g(Un)n(balanced)g (Ratio)p 752 4080 V 750 4180 4 100 v 802 4150 a(Ratio)p 2129 4180 V 2146 4180 V 1195 w(Av)n(e)p 2393 4180 V 106 w(Std)p 2640 4180 V 123 w(Min)p 2885 4180 V 100 w(Max)p 3146 4180 V 752 4183 2396 4 v 750 4283 4 100 v 802 4253 a(Width)i(/)e(Width)p 2129 4283 V 2146 4283 V 833 w(2.1)p 2393 4283 V 140 w(0.3)p 2640 4283 V 140 w(1.1)p 2885 4283 V 138 w(3.0)p 3146 4283 V 752 4286 2396 4 v 750 4386 4 100 v 802 4356 a(Cutset)h(Width)h(/)e(Cutset)h(Width)p 2129 4386 V 2146 4386 V 297 w(1.5)p 2393 4386 V 140 w(0.4)p 2640 4386 V 140 w(0.9)p 2885 4386 V 138 w(3.5)p 3146 4386 V 752 4389 2396 4 v 750 4489 4 100 v 802 4459 a(Con)n(text)f (Width)i(/)e(Con)n(text)h(Width)p 2129 4489 V 2146 4489 V 196 w(1.6)p 2393 4489 V 140 w(0.2)p 2640 4489 V 140 w(1.0)p 2885 4489 V 138 w(2.0)p 3146 4489 V 752 4492 2396 4 v 750 4592 4 100 v 802 4562 a(A-Cutset)g(Width)h(/)e(A-Cutset)h (Width)p 2129 4592 V 2146 4592 V 117 w(0.6)p 2393 4592 V 140 w(0.2)p 2640 4592 V 140 w(0.2)p 2885 4592 V 138 w(1.0)p 3146 4592 V 752 4595 2396 4 v 752 4612 V 750 4711 4 100 v 802 4682 a(Cutset)g(Width)h(/)e(Width)p 2129 4711 V 2146 4711 V 565 w(0.6)p 2393 4711 V 140 w(0.2)p 2640 4711 V 140 w(0.5)p 2885 4711 V 138 w(1.5)p 3146 4711 V 752 4715 2396 4 v 750 4814 4 100 v 802 4784 a(A-Cutset)h(Width)h (/)e(Width)p 2129 4814 V 2146 4814 V 475 w(3.5)p 2393 4814 V 140 w(0.7)p 2640 4814 V 140 w(2.0)p 2885 4814 V 138 w(6.0)p 3146 4814 V 752 4818 2396 4 v 1421 5050 a(Figure)g(19:)36 b Ff(Set-A)27 b FE(net)n(w)n(orks.)1908 5656 y(23)p eop %%Page: 24 24 24 23 bop 651 2250 a @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 3118 @rwi @setspecial %%BeginDocument: widths75.ps %!PS-Adobe-2.0 EPSF-2.0 %%Title: c:/windows/desktop/rc/results/n15075/widths.ps %%Creator: gnuplot 3.7 patchlevel 0 %%CreationDate: Thu Jul 22 11:38:09 1999 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -53 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /UL { gnulinewidth mul /userlinewidth exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Latex) findfont 160 scalefont setfont 1.000 UL LTb 624 480 M 63 0 V 6241 0 R -63 0 V 528 480 M (0) Rshow 624 888 M 63 0 V 6241 0 R -63 0 V 528 888 M (5) Rshow 624 1296 M 63 0 V 6241 0 R -63 0 V -6337 0 R (10) Rshow 624 1704 M 63 0 V 6241 0 R -63 0 V -6337 0 R (15) Rshow 624 2112 M 63 0 V 6241 0 R -63 0 V -6337 0 R (20) Rshow 624 2520 M 63 0 V 6241 0 R -63 0 V -6337 0 R (25) Rshow 624 2928 M 63 0 V 6241 0 R -63 0 V -6337 0 R (30) Rshow 624 3336 M 63 0 V 6241 0 R -63 0 V -6337 0 R (35) Rshow 624 3744 M 63 0 V 6241 0 R -63 0 V -6337 0 R (40) Rshow 624 4152 M 63 0 V 6241 0 R -63 0 V -6337 0 R (45) Rshow 624 4560 M 63 0 V 6241 0 R -63 0 V -6337 0 R (50) Rshow 624 480 M 0 63 V 0 4017 R 0 -63 V 624 320 M (0) Cshow 1254 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (100) Cshow 1885 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (200) Cshow 2515 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (300) Cshow 3146 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (400) Cshow 3776 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (500) Cshow 4406 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (600) Cshow 5037 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (700) Cshow 5667 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (800) Cshow 6298 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (900) Cshow 6928 480 M 0 63 V 0 4017 R 0 -63 V 0 -4177 R (1000) Cshow 1.000 UL LTb 624 480 M 6304 0 V 0 4080 V -6304 0 V 624 480 L 160 2520 M currentpoint gsave translate 90 rotate 0 0 M (Width) Cshow grestore 3776 80 M (Samples) Cshow 3776 4800 M (Distribution of 1000 Random Networks --- Set B) Cshow 1.000 UP 1.000 UL LT0 624 1296 Pls 630 3418 Pls 637 3091 Pls 643 3010 Pls 649 2357 Pls 656 1214 Pls 662 970 Pls 668 3581 Pls 674 1378 Pls 681 1296 Pls 687 2194 Pls 693 2030 Pls 700 3254 Pls 706 1051 Pls 712 2030 Pls 719 1867 Pls 725 3826 Pls 731 3173 Pls 737 1541 Pls 744 3826 Pls 750 3173 Pls 756 2846 Pls 763 2520 Pls 769 1867 Pls 775 4070 Pls 782 2765 Pls 788 725 Pls 794 2275 Pls 801 2112 Pls 807 2275 Pls 813 1541 Pls 819 2030 Pls 826 3010 Pls 832 806 Pls 838 1459 Pls 845 3254 Pls 851 2194 Pls 857 3826 Pls 864 3173 Pls 870 3173 Pls 876 2357 Pls 882 970 Pls 889 3907 Pls 895 3254 Pls 901 1622 Pls 908 3091 Pls 914 2357 Pls 920 1541 Pls 927 2357 Pls 933 3418 Pls 939 2602 Pls 946 1133 Pls 952 3989 Pls 958 2438 Pls 964 2194 Pls 971 1378 Pls 977 3662 Pls 983 3336 Pls 990 1622 Pls 996 3336 Pls 1002 2765 Pls 1009 643 Pls 1015 3254 Pls 1021 3826 Pls 1027 1704 Pls 1034 1214 Pls 1040 2030 Pls 1046 3744 Pls 1053 3418 Pls 1059 2194 Pls 1065 1786 Pls 1072 1949 Pls 1078 1133 Pls 1084 1459 Pls 1090 1051 Pls 1097 2928 Pls 1103 2194 Pls 1109 3826 Pls 1116 643 Pls 1122 2846 Pls 1128 3336 Pls 1135 1214 Pls 1141 1704 Pls 1147 1214 Pls 1154 2438 Pls 1160 888 Pls 1166 3662 Pls 1172 1214 Pls 1179 2112 Pls 1185 2928 Pls 1191 1786 Pls 1198 3173 Pls 1204 3010 Pls 1210 3173 Pls 1217 1867 Pls 1223 3499 Pls 1229 3091 Pls 1235 3744 Pls 1242 2275 Pls 1248 3744 Pls 1254 1949 Pls 1261 1296 Pls 1267 1296 Pls 1273 3499 Pls 1280 3010 Pls 1286 2765 Pls 1292 1949 Pls 1299 3091 Pls 1305 1622 Pls 1311 1214 Pls 1317 2438 Pls 1324 643 Pls 1330 1133 Pls 1336 2438 Pls 1343 1949 Pls 1349 3254 Pls 1355 1214 Pls 1362 1704 Pls 1368 1296 Pls 1374 3744 Pls 1380 2846 Pls 1387 3091 Pls 1393 725 Pls 1399 3091 Pls 1406 1133 Pls 1412 3744 Pls 1418 3010 Pls 1425 3336 Pls 1431 3826 Pls 1437 3581 Pls 1444 1459 Pls 1450 3254 Pls 1456 3499 Pls 1462 2438 Pls 1469 3091 Pls 1475 1867 Pls 1481 3418 Pls 1488 3744 Pls 1494 3091 Pls 1500 2357 Pls 1507 2438 Pls 1513 2030 Pls 1519 1867 Pls 1525 2357 Pls 1532 1459 Pls 1538 1622 Pls 1544 1541 Pls 1551 3254 Pls 1557 3907 Pls 1563 3010 Pls 1570 3581 Pls 1576 1133 Pls 1582 3418 Pls 1589 3336 Pls 1595 1541 Pls 1601 1622 Pls 1607 970 Pls 1614 2683 Pls 1620 3744 Pls 1626 1378 Pls 1633 2030 Pls 1639 1541 Pls 1645 1296 Pls 1652 3499 Pls 1658 2275 Pls 1664 1622 Pls 1670 2846 Pls 1677 1296 Pls 1683 725 Pls 1689 643 Pls 1696 3581 Pls 1702 2357 Pls 1708 2112 Pls 1715 2275 Pls 1721 1214 Pls 1727 2846 Pls 1734 3173 Pls 1740 888 Pls 1746 3173 Pls 1752 2275 Pls 1759 3254 Pls 1765 3254 Pls 1771 3010 Pls 1778 3336 Pls 1784 3826 Pls 1790 1786 Pls 1797 2765 Pls 1803 2765 Pls 1809 2438 Pls 1815 3418 Pls 1822 3662 Pls 1828 3662 Pls 1834 3499 Pls 1841 1133 Pls 1847 3744 Pls 1853 2275 Pls 1860 2030 Pls 1866 3173 Pls 1872 2846 Pls 1878 1704 Pls 1885 1296 Pls 1891 643 Pls 1897 1051 Pls 1904 3662 Pls 1910 3010 Pls 1916 888 Pls 1923 3662 Pls 1929 806 Pls 1935 2194 Pls 1942 3499 Pls 1948 3091 Pls 1954 1949 Pls 1960 3662 Pls 1967 2357 Pls 1973 2846 Pls 1979 1378 Pls 1986 1378 Pls 1992 3173 Pls 1998 3826 Pls 2005 2520 Pls 2011 1133 Pls 2017 2194 Pls 2023 3091 Pls 2030 1459 Pls 2036 3581 Pls 2042 1133 Pls 2049 2602 Pls 2055 1867 Pls 2061 3581 Pls 2068 3826 Pls 2074 4152 Pls 2080 2112 Pls 2087 1622 Pls 2093 2112 Pls 2099 1622 Pls 2105 3173 Pls 2112 3418 Pls 2118 2765 Pls 2124 3173 Pls 2131 2357 Pls 2137 1214 Pls 2143 2928 Pls 2150 3336 Pls 2156 2438 Pls 2162 2520 Pls 2168 2438 Pls 2175 2357 Pls 2181 2846 Pls 2187 3826 Pls 2194 1459 Pls 2200 1622 Pls 2206 3662 Pls 2213 2520 Pls 2219 3744 Pls 2225 806 Pls 2232 3173 Pls 2238 1704 Pls 2244 1949 Pls 2250 2275 Pls 2257 2112 Pls 2263 3989 Pls 2269 2112 Pls 2276 3010 Pls 2282 3336 Pls 2288 2275 Pls 2295 1867 Pls 2301 1949 Pls 2307 3173 Pls 2313 1786 Pls 2320 1214 Pls 2326 3499 Pls 2332 1622 Pls 2339 3010 Pls 2345 2357 Pls 2351 2683 Pls 2358 2030 Pls 2364 970 Pls 2370 1622 Pls 2377 3010 Pls 2383 1867 Pls 2389 1622 Pls 2395 2357 Pls 2402 2438 Pls 2408 1949 Pls 2414 2030 Pls 2421 725 Pls 2427 1786 Pls 2433 1867 Pls 2440 3173 Pls 2446 3010 Pls 2452 2602 Pls 2458 1786 Pls 2465 1867 Pls 2471 3826 Pls 2477 2928 Pls 2484 2765 Pls 2490 888 Pls 2496 1704 Pls 2503 1704 Pls 2509 1704 Pls 2515 1133 Pls 2522 2683 Pls 2528 1214 Pls 2534 2928 Pls 2540 2602 Pls 2547 2438 Pls 2553 3662 Pls 2559 3418 Pls 2566 3254 Pls 2572 3581 Pls 2578 3662 Pls 2585 1133 Pls 2591 1867 Pls 2597 1867 Pls 2603 2438 Pls 2610 1133 Pls 2616 3581 Pls 2622 2520 Pls 2629 4478 Pls 2635 1214 Pls 2641 2683 Pls 2648 1541 Pls 2654 2112 Pls 2660 3826 Pls 2666 1949 Pls 2673 3826 Pls 2679 2030 Pls 2685 2683 Pls 2692 2846 Pls 2698 3010 Pls 2704 3254 Pls 2711 3662 Pls 2717 3091 Pls 2723 3662 Pls 2730 3581 Pls 2736 1786 Pls 2742 725 Pls 2748 3418 Pls 2755 3010 Pls 2761 2846 Pls 2767 3907 Pls 2774 4152 Pls 2780 1296 Pls 2786 1378 Pls 2793 4397 Pls 2799 1459 Pls 2805 1378 Pls 2811 2275 Pls 2818 1704 Pls 2824 2194 Pls 2830 2438 Pls 2837 3254 Pls 2843 1949 Pls 2849 806 Pls 2856 3581 Pls 2862 2357 Pls 2868 3499 Pls 2875 643 Pls 2881 3091 Pls 2887 2602 Pls 2893 3254 Pls 2900 643 Pls 2906 3091 Pls 2912 2275 Pls 2919 888 Pls 2925 1214 Pls 2931 2438 Pls 2938 1622 Pls 2944 3173 Pls 2950 1214 Pls 2956 1214 Pls 2963 3173 Pls 2969 970 Pls 2975 725 Pls 2982 3010 Pls 2988 1133 Pls 2994 2438 Pls 3001 1704 Pls 3007 3173 Pls 3013 1133 Pls 3020 1867 Pls 3026 2846 Pls 3032 3336 Pls 3038 2928 Pls 3045 2438 Pls 3051 888 Pls 3057 3336 Pls 3064 1622 Pls 3070 1867 Pls 3076 3826 Pls 3083 970 Pls 3089 2357 Pls 3095 1378 Pls 3101 3336 Pls 3108 2846 Pls 3114 1296 Pls 3120 2194 Pls 3127 725 Pls 3133 3662 Pls 3139 3336 Pls 3146 1786 Pls 3152 2765 Pls 3158 2602 Pls 3165 1459 Pls 3171 1949 Pls 3177 2602 Pls 3183 3662 Pls 3190 3173 Pls 3196 1296 Pls 3202 2683 Pls 3209 3662 Pls 3215 3173 Pls 3221 2194 Pls 3228 2520 Pls 3234 3418 Pls 3240 3336 Pls 3246 2683 Pls 3253 3581 Pls 3259 2438 Pls 3265 1786 Pls 3272 2357 Pls 3278 3499 Pls 3284 1622 Pls 3291 2112 Pls 3297 3662 Pls 3303 1296 Pls 3310 888 Pls 3316 2928 Pls 3322 1378 Pls 3328 3091 Pls 3335 3254 Pls 3341 3907 Pls 3347 1949 Pls 3354 3010 Pls 3360 3581 Pls 3366 3499 Pls 3373 3336 Pls 3379 2194 Pls 3385 3336 Pls 3391 2112 Pls 3398 3091 Pls 3404 1786 Pls 3410 2928 Pls 3417 1541 Pls 3423 3091 Pls 3429 1296 Pls 3436 2112 Pls 3442 3744 Pls 3448 2275 Pls 3454 1051 Pls 3461 1541 Pls 3467 1949 Pls 3473 2112 Pls 3480 2357 Pls 3486 1949 Pls 3492 3010 Pls 3499 1214 Pls 3505 3662 Pls 3511 3173 Pls 3518 1459 Pls 3524 3173 Pls 3530 2438 Pls 3536 2275 Pls 3543 1296 Pls 3549 1378 Pls 3555 3173 Pls 3562 3173 Pls 3568 2357 Pls 3574 2030 Pls 3581 3418 Pls 3587 3254 Pls 3593 2194 Pls 3599 2765 Pls 3606 3907 Pls 3612 2112 Pls 3618 4070 Pls 3625 3010 Pls 3631 3173 Pls 3637 3254 Pls 3644 2112 Pls 3650 3418 Pls 3656 2194 Pls 3663 1378 Pls 3669 3662 Pls 3675 2194 Pls 3681 2928 Pls 3688 2357 Pls 3694 2357 Pls 3700 3173 Pls 3707 888 Pls 3713 643 Pls 3719 2928 Pls 3726 3581 Pls 3732 3418 Pls 3738 2357 Pls 3744 3907 Pls 3751 2765 Pls 3757 1214 Pls 3763 3499 Pls 3770 3254 Pls 3776 3254 Pls 3782 2683 Pls 3789 1214 Pls 3795 1296 Pls 3801 1378 Pls 3808 3010 Pls 3814 3744 Pls 3820 3989 Pls 3826 1133 Pls 3833 1949 Pls 3839 1296 Pls 3845 3173 Pls 3852 3744 Pls 3858 1867 Pls 3864 2194 Pls 3871 806 Pls 3877 1459 Pls 3883 2765 Pls 3889 2928 Pls 3896 725 Pls 3902 3091 Pls 3908 1459 Pls 3915 1296 Pls 3921 3581 Pls 3927 3173 Pls 3934 2438 Pls 3940 3989 Pls 3946 2928 Pls 3953 3907 Pls 3959 1133 Pls 3965 2194 Pls 3971 3254 Pls 3978 2112 Pls 3984 2602 Pls 3990 3581 Pls 3997 2438 Pls 4003 1459 Pls 4009 3418 Pls 4016 2112 Pls 4022 725 Pls 4028 1051 Pls 4034 1949 Pls 4041 3826 Pls 4047 3989 Pls 4053 1786 Pls 4060 2357 Pls 4066 3826 Pls 4072 1214 Pls 4079 2683 Pls 4085 1704 Pls 4091 1867 Pls 4098 2194 Pls 4104 3826 Pls 4110 3907 Pls 4116 1786 Pls 4123 3254 Pls 4129 3336 Pls 4135 3662 Pls 4142 3254 Pls 4148 3010 Pls 4154 3418 Pls 4161 3581 Pls 4167 2683 Pls 4173 2928 Pls 4179 1459 Pls 4186 3254 Pls 4192 2520 Pls 4198 1133 Pls 4205 1378 Pls 4211 2194 Pls 4217 3826 Pls 4224 1378 Pls 4230 3989 Pls 4236 2602 Pls 4242 2683 Pls 4249 2030 Pls 4255 1704 Pls 4261 3499 Pls 4268 1214 Pls 4274 3581 Pls 4280 2112 Pls 4287 2846 Pls 4293 1786 Pls 4299 3581 Pls 4306 1459 Pls 4312 2928 Pls 4318 2357 Pls 4324 2602 Pls 4331 2275 Pls 4337 3662 Pls 4343 3091 Pls 4350 2602 Pls 4356 2846 Pls 4362 2030 Pls 4369 3418 Pls 4375 3826 Pls 4381 3499 Pls 4387 3499 Pls 4394 2275 Pls 4400 3907 Pls 4406 1949 Pls 4413 3254 Pls 4419 1949 Pls 4425 3581 Pls 4432 2357 Pls 4438 2357 Pls 4444 2602 Pls 4451 1459 Pls 4457 1051 Pls 4463 2928 Pls 4469 3091 Pls 4476 3499 Pls 4482 1541 Pls 4488 1378 Pls 4495 2520 Pls 4501 3091 Pls 4507 2357 Pls 4514 1786 Pls 4520 1622 Pls 4526 1214 Pls 4532 1296 Pls 4539 2846 Pls 4545 2928 Pls 4551 4234 Pls 4558 643 Pls 4564 2194 Pls 4570 1949 Pls 4577 3173 Pls 4583 1051 Pls 4589 1459 Pls 4596 725 Pls 4602 3418 Pls 4608 1704 Pls 4614 2683 Pls 4621 3499 Pls 4627 970 Pls 4633 2030 Pls 4640 2030 Pls 4646 643 Pls 4652 2928 Pls 4659 3581 Pls 4665 1867 Pls 4671 1296 Pls 4677 3581 Pls 4684 2112 Pls 4690 3254 Pls 4696 3662 Pls 4703 3499 Pls 4709 1459 Pls 4715 1867 Pls 4722 1214 Pls 4728 3010 Pls 4734 1622 Pls 4741 2765 Pls 4747 1622 Pls 4753 1622 Pls 4759 2602 Pls 4766 3010 Pls 4772 3907 Pls 4778 3091 Pls 4785 3336 Pls 4791 1459 Pls 4797 2683 Pls 4804 2765 Pls 4810 3091 Pls 4816 2030 Pls 4822 1214 Pls 4829 2112 Pls 4835 1051 Pls 4841 4234 Pls 4848 4070 Pls 4854 1296 Pls 4860 2438 Pls 4867 3336 Pls 4873 3091 Pls 4879 2357 Pls 4886 1541 Pls 4892 2846 Pls 4898 3826 Pls 4904 1949 Pls 4911 1704 Pls 4917 2602 Pls 4923 2112 Pls 4930 1949 Pls 4936 3336 Pls 4942 3581 Pls 4949 3581 Pls 4955 3091 Pls 4961 3173 Pls 4967 2683 Pls 4974 1051 Pls 4980 1133 Pls 4986 1867 Pls 4993 2928 Pls 4999 3336 Pls 5005 3010 Pls 5012 2194 Pls 5018 3336 Pls 5024 2438 Pls 5030 806 Pls 5037 3254 Pls 5043 3989 Pls 5049 1214 Pls 5056 3499 Pls 5062 1622 Pls 5068 3744 Pls 5075 3662 Pls 5081 1867 Pls 5087 725 Pls 5094 2602 Pls 5100 3336 Pls 5106 2030 Pls 5112 2683 Pls 5119 2520 Pls 5125 2683 Pls 5131 2765 Pls 5138 725 Pls 5144 2846 Pls 5150 725 Pls 5157 1949 Pls 5163 2765 Pls 5169 1378 Pls 5175 643 Pls 5182 1051 Pls 5188 2275 Pls 5194 2520 Pls 5201 2765 Pls 5207 1133 Pls 5213 1214 Pls 5220 3173 Pls 5226 2030 Pls 5232 1541 Pls 5239 1786 Pls 5245 4315 Pls 5251 2357 Pls 5257 2112 Pls 5264 3336 Pls 5270 1378 Pls 5276 1296 Pls 5283 1296 Pls 5289 2683 Pls 5295 1051 Pls 5302 2602 Pls 5308 1459 Pls 5314 3173 Pls 5320 1378 Pls 5327 1459 Pls 5333 1378 Pls 5339 3336 Pls 5346 1214 Pls 5352 1459 Pls 5358 3010 Pls 5365 1867 Pls 5371 3581 Pls 5377 3907 Pls 5384 3010 Pls 5390 1296 Pls 5396 1378 Pls 5402 2030 Pls 5409 2928 Pls 5415 4070 Pls 5421 3662 Pls 5428 2438 Pls 5434 1704 Pls 5440 3581 Pls 5447 2438 Pls 5453 1541 Pls 5459 3091 Pls 5465 3336 Pls 5472 3744 Pls 5478 3826 Pls 5484 3499 Pls 5491 3907 Pls 5497 1786 Pls 5503 3826 Pls 5510 3173 Pls 5516 2275 Pls 5522 3662 Pls 5529 4152 Pls 5535 2846 Pls 5541 2275 Pls 5547 3010 Pls 5554 1541 Pls 5560 2683 Pls 5566 2765 Pls 5573 3826 Pls 5579 3173 Pls 5585 3826 Pls 5592 1214 Pls 5598 2030 Pls 5604 3173 Pls 5610 3336 Pls 5617 2438 Pls 5623 3499 Pls 5629 1622 Pls 5636 1459 Pls 5642 3662 Pls 5648 2928 Pls 5655 2357 Pls 5661 970 Pls 5667 643 Pls 5674 3581 Pls 5680 3254 Pls 5686 1459 Pls 5692 3091 Pls 5699 3173 Pls 5705 1051 Pls 5711 2357 Pls 5718 3907 Pls 5724 1296 Pls 5730 3091 Pls 5737 643 Pls 5743 3336 Pls 5749 888 Pls 5755 4315 Pls 5762 1133 Pls 5768 1133 Pls 5774 2928 Pls 5781 3581 Pls 5787 3581 Pls 5793 2928 Pls 5800 3499 Pls 5806 3499 Pls 5812 1378 Pls 5818 2765 Pls 5825 1378 Pls 5831 970 Pls 5837 2928 Pls 5844 3254 Pls 5850 1786 Pls 5856 2357 Pls 5863 3254 Pls 5869 2030 Pls 5875 1541 Pls 5882 3336 Pls 5888 1541 Pls 5894 3173 Pls 5900 1214 Pls 5907 1051 Pls 5913 2683 Pls 5919 888 Pls 5926 1051 Pls 5932 1704 Pls 5938 1867 Pls 5945 2683 Pls 5951 3581 Pls 5957 1541 Pls 5963 1786 Pls 5970 1459 Pls 5976 1704 Pls 5982 2520 Pls 5989 2030 Pls 5995 1459 Pls 6001 3581 Pls 6008 3091 Pls 6014 3254 Pls 6020 3662 Pls 6027 2520 Pls 6033 806 Pls 6039 2194 Pls 6045 3254 Pls 6052 3254 Pls 6058 1949 Pls 6064 3010 Pls 6071 2520 Pls 6077 3010 Pls 6083 1214 Pls 6090 2357 Pls 6096 3091 Pls 6102 1378 Pls 6108 1133 Pls 6115 970 Pls 6121 2275 Pls 6127 2438 Pls 6134 3254 Pls 6140 3662 Pls 6146 725 Pls 6153 3173 Pls 6159 2030 Pls 6165 3418 Pls 6172 3989 Pls 6178 2765 Pls 6184 2846 Pls 6190 3499 Pls 6197 3744 Pls 6203 1704 Pls 6209 1867 Pls 6216 1541 Pls 6222 2846 Pls 6228 1786 Pls 6235 2765 Pls 6241 1622 Pls 6247 3662 Pls 6253 725 Pls 6260 3744 Pls 6266 2846 Pls 6272 1214 Pls 6279 1214 Pls 6285 3826 Pls 6291 1214 Pls 6298 3173 Pls 6304 2520 Pls 6310 2520 Pls 6317 1051 Pls 6323 3254 Pls 6329 2683 Pls 6335 3173 Pls 6342 3173 Pls 6348 2846 Pls 6354 3173 Pls 6361 2520 Pls 6367 3662 Pls 6373 3091 Pls 6380 2928 Pls 6386 3418 Pls 6392 3254 Pls 6398 3010 Pls 6405 2683 Pls 6411 3091 Pls 6417 2765 Pls 6424 3989 Pls 6430 2030 Pls 6436 2194 Pls 6443 3336 Pls 6449 2112 Pls 6455 2765 Pls 6462 3662 Pls 6468 3336 Pls 6474 1378 Pls 6480 3826 Pls 6487 806 Pls 6493 3173 Pls 6499 888 Pls 6506 1296 Pls 6512 1133 Pls 6518 1704 Pls 6525 4152 Pls 6531 3010 Pls 6537 1541 Pls 6543 970 Pls 6550 1786 Pls 6556 2438 Pls 6562 2602 Pls 6569 3581 Pls 6575 2275 Pls 6581 2275 Pls 6588 1133 Pls 6594 2683 Pls 6600 970 Pls 6606 1214 Pls 6613 1704 Pls 6619 1541 Pls 6625 3173 Pls 6632 888 Pls 6638 2765 Pls 6644 3826 Pls 6651 2765 Pls 6657 1051 Pls 6663 2030 Pls 6670 2602 Pls 6676 2765 Pls 6682 2112 Pls 6688 3254 Pls 6695 2520 Pls 6701 2194 Pls 6707 3581 Pls 6714 3336 Pls 6720 3091 Pls 6726 888 Pls 6733 3173 Pls 6739 3336 Pls 6745 2520 Pls 6751 3336 Pls 6758 3254 Pls 6764 725 Pls 6770 2765 Pls 6777 3336 Pls 6783 1704 Pls 6789 2194 Pls 6796 3581 Pls 6802 1622 Pls 6808 3826 Pls 6815 3336 Pls 6821 3254 Pls 6827 2765 Pls 6833 3254 Pls 6840 2112 Pls 6846 3336 Pls 6852 1296 Pls 6859 2438 Pls 6865 888 Pls 6871 1378 Pls 6878 2275 Pls 6884 2602 Pls 6890 2112 Pls 6896 3336 Pls 6903 3254 Pls 6909 1704 Pls 6915 3010 Pls 6922 1051 Pls stroke grestore end showpage %%Trailer %%DocumentFonts: Latex %%EndDocument @endspecial 1607 2613 a FE(Un)n(balanced)27 b(Dtrees)p 737 2646 2426 4 v 735 2745 4 100 v 787 2716 a(P)n(arameter)p 2114 2745 V 2131 2745 V 1015 w(Av)n(e)p 2378 2745 V 106 w(Std)p 2625 2745 V 123 w(Min)p 2872 2745 V 103 w(Max)p 3161 2745 V 737 2749 2426 4 v 735 2848 4 100 v 787 2819 a(Width)p 2114 2848 V 2131 2848 V 1163 w(24.2)p 2378 2848 V 98 w(11.5)p 2625 2848 V 98 w(2.0)p 2872 2848 V 141 w(49.0)p 3161 2848 V 737 2852 2426 4 v 735 2951 4 100 v 787 2921 a(Cutset)h(Width)p 2114 2951 V 2131 2951 V 895 w(12.4)p 2378 2951 V 98 w(6.4)p 2625 2951 V 140 w(2.0)p 2872 2951 V 141 w(32.0)p 3161 2951 V 737 2955 2426 4 v 735 3054 4 100 v 787 3024 a(Con)n(text)f(Width)p 2114 3054 V 2131 3054 V 845 w(23.2)p 2378 3054 V 98 w(10.6)p 2625 3054 V 98 w(3.0)p 2872 3054 V 141 w(46.0)p 3161 3054 V 737 3058 2426 4 v 735 3157 4 100 v 787 3127 a(A-Cutset)h(Width)p 2114 3157 V 2131 3157 V 805 w(62.4)p 2378 3157 V 98 w(15.4)p 2625 3157 V 98 w(10.0)p 2872 3157 V 99 w(138.0)p 3161 3157 V 737 3161 2426 4 v 1653 3330 a(Balanced)f(Dtrees)p 737 3363 V 735 3463 4 100 v 787 3433 a(P)n(arameter)p 2114 3463 V 2131 3463 V 1015 w(Av)n(e)p 2378 3463 V 106 w(Std)p 2625 3463 V 123 w(Min)p 2872 3463 V 103 w(Max)p 3161 3463 V 737 3466 2426 4 v 735 3566 4 100 v 787 3536 a(Width)p 2114 3566 V 2131 3566 V 1163 w(33.5)p 2378 3566 V 98 w(10.5)p 2625 3566 V 98 w(3.0)p 2872 3566 V 141 w(55.0)p 3161 3566 V 737 3569 2426 4 v 735 3669 4 100 v 787 3639 a(Cutset)h(Width)p 2114 3669 V 2131 3669 V 895 w(17.1)p 2378 3669 V 98 w(7.8)p 2625 3669 V 140 w(2.0)p 2872 3669 V 141 w(43.0)p 3161 3669 V 737 3672 2426 4 v 735 3772 4 100 v 787 3742 a(Con)n(text)f(Width)p 2114 3772 V 2131 3772 V 845 w(29.9)p 2378 3772 V 98 w(10.4)p 2625 3772 V 98 w(4.0)p 2872 3772 V 141 w(55.0)p 3161 3772 V 737 3775 2426 4 v 735 3875 4 100 v 787 3845 a(A-Cutset)h(Width)p 2114 3875 V 2131 3875 V 805 w(47.9)p 2378 3875 V 98 w(11.3)p 2625 3875 V 98 w(7.0)p 2872 3875 V 141 w(73.0)p 3161 3875 V 737 3878 2426 4 v 1410 4047 a(Balanced)f(/)g(Un)n(balanced)g (Ratio)p 737 4080 V 735 4180 4 100 v 787 4150 a(Ratio)p 2114 4180 V 2131 4180 V 1195 w(Av)n(e)p 2378 4180 V 106 w(Std)p 2625 4180 V 123 w(Min)p 2872 4180 V 103 w(Max)p 3161 4180 V 737 4183 2426 4 v 735 4283 4 100 v 787 4253 a(Width)i(/)e(Width)p 2114 4283 V 2131 4283 V 833 w(1.6)p 2378 4283 V 140 w(0.5)p 2625 4283 V 140 w(1.0)p 2872 4283 V 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(elimination)g(order)f(of)h(width)h Fw(w)r FE(,)g Ff(el2dt)f FE(will)g(construct)g(a)g(dtree)f(of)h(cutset)h(width)g Fv(\024)25 b Fw(w)32 b FE(\(Theorem)c(8\).)0 3754 y Ff(bal-dt)f FE(will)f(balance)g(the)h(dtree,)g(while)g(ensuring)e(that)i(its)g (cutset)g(width)g(is)g Fv(\024)22 b Fw(w)30 b FE(\(Theorem)c(9\).)36 b(Since)27 b(the)g(heigh)n(t)f(of)0 3854 y(the)h(balanced)g(dtree)f(is) h Fw(O)r FE(\(log)15 b Fw(n)p FE(\),)28 b(its)f(a-cutset)f(width)i(m)n (ust)f(b)r(e)g Fw(O)r FE(\()p Fw(w)18 b FE(log)c Fw(n)p FE(\))27 b(b)n(y)g(Theorem)f(2.)36 b(Therefore,)26 b(the)h(n)n(um)n(b)r (er)0 3954 y(of)j(recursiv)n(e)f(calls)h(made)g(b)n(y)h Ff(r)n(c1)f FE(to)h(no)r(de)f Fw(T)42 b FE(is)30 b Fw(O)r FE(\(exp)q(\()p Fw(w)17 b FE(log)d Fw(n)p FE(\)\).)46 b(The)31 b(total)f(n)n(um)n(b)r(er)g(of)g(recursiv)n(e)f(calls)h(made)g (b)n(y)0 4053 y Ff(r)n(c1)e FE(is)f(then)h Fw(O)r FE(\()p Fw(n)14 b FE(exp)q(\()p Fw(w)j FE(log)d Fw(n)p FE(\)\).)p 1126 4028 V 1126 4078 4 50 v 1170 4078 V 1126 4081 48 4 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Fu(cutset)o FE(\()p Fw(T)2695 4994 y Fj(p)2733 5024 y FE(\))2765 4994 y Fq(#)2824 5024 y Fu(context)o FE(\()p Fw(T)3173 4994 y Fj(p)3211 5024 y FE(\))3243 4994 y Fq(#)3302 5024 y FE(.)36 b(Since)25 b(the)g(dtree)0 5123 y(is)30 b(constructed)f(using)g Ff(el2dt)p FE(,)h Fu(cutset)o FE(\()p Fw(T)1345 5093 y Fj(p)1383 5123 y FE(\))1415 5093 y Fq(#)1474 5123 y Fu(context)p FE(\()p Fw(T)1824 5093 y Fj(p)1861 5123 y FE(\))1893 5093 y Fq(#)1979 5123 y FE(=)c Fw(O)r FE(\(exp\()p Fw(w)r FE(\)\))32 b(\(Theorem)d(8\).)43 b(Hence,)30 b(the)g(total)f(n)n (um)n(b)r(er)0 5223 y(of)f(recursiv)n(e)d(calls)i(is)h Fw(O)r FE(\()p Fw(n)14 b FE(exp\()p Fw(w)r FE(\)\).)p 1208 5198 V 1208 5248 4 50 v 1251 5248 V 1208 5251 48 4 v 0 5276 1560 4 v 62 5330 a Fo(13)127 5353 y Fn(W)-6 b(e)24 b(are)g(assuming)f(that)i(cutset)g(and)f(con)n(text)i(sizes)d (are)h(b)r(ounded)h(b)n(y)f(constan)n(ts.)1908 5656 y FE(25)p eop %%Page: 26 26 26 25 bop 0 90 a Fb(Pro)s(of)37 b(of)h(Theorem)f(6)0 243 y FE(The)26 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FE(\)\)\()p Fu(context)q FE(\()p Fw(T)1211 2415 y Fj(p)1248 2445 y FE(\))19 b Fv(\000)f Fu(context)o FE(\()p Fw(T)12 b FE(\)\))1795 2415 y Fq(#)1882 2445 y FE(are)26 b(non{cac)n(hed.)208 2601 y(This)h(follo)n(ws)g(b)r (ecause)g(eac)n(h)g Fw(T)1225 2571 y Fj(p)1262 2601 y FE({t)n(yp)r(e)g(is)h(equally)f(lik)n(ely)g(to)g(b)r(e)h(cac)n(hed.)37 b(Moreo)n(v)n(er,)321 2757 y(-)k(A)h(cac)n(hed)e Fw(T)838 2727 y Fj(p)876 2757 y FE({t)n(yp)r(e)h Ft(x)h FE(will)f(generate)f Fu(cutset)p FE(\()p Fw(T)2028 2727 y Fj(p)2065 2757 y FE(\))2097 2727 y Fq(#)2198 2757 y FE(calls)g(to)h(no)r(de)h Fw(T)52 b FE(since)41 b Ff(r)n(c)q FE(\()p Fw(T)3235 2727 y Fj(p)3272 2757 y FE(\))h(will)f(recurse)f(on)390 2857 y Fx(only)h(one)e FE(call)f(p)r(er)g(cac)n(hed)g Fw(T)1408 2827 y Fj(p)1445 2857 y FE({t)n(yp)r(e.)70 b(Only)38 b(one)g(of)h(these)f(calls)g(is)h(consisten)n(t)f(with)h Fw(T)12 b FE({t)n(yp)r(e)37 b Ft(y)j FE(since)390 2957 y Fu(cutset)p FE(\()p Fw(T)692 2926 y Fj(p)729 2957 y FE(\))24 b Fv(\022)e 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FE({t)n(yp)r(e)g(consisten)n(t)h (with)208 3534 y Ft(y)q FE(.)37 b(Therefore,)273 3692 y Fu(acpt)o FE(\()p Fw(T)12 b FE(\))83 b(=)189 b Fu(cf)6 b FE(\()p Fw(T)1045 3658 y Fj(p)1082 3692 y FE(\)\()p Fu(context)p FE(\()p Fw(T)1496 3658 y Fj(p)1534 3692 y FE(\))19 b Fv(\000)f Fu(context)o FE(\()p Fw(T)12 b FE(\)\))2081 3658 y Fq(#)884 3748 y Fs(|)p 921 3748 554 10 v 554 w({z)p 1549 3748 V 554 w(})778 3849 y FE(\(no.)37 b(cac)n(hed)26 b Fw(T)1288 3819 y Fj(p)1326 3849 y FE({t)n(yp)r(es)h (consisten)n(t)g(with)h Ft(y)q FE(\))2932 3692 y(1)2878 3727 y Fs(|{z})2260 3828 y FE(\(no.)37 b(calls)27 b(in)h Fw(T)12 b FE({t)n(yp)r(e)26 b Ft(y)j FE(eac)n(h)e(generates\))3660 3692 y(+)868 3986 y(\(1)18 b Fv(\000)g Fu(cf)6 b FE(\()p Fw(T)1204 3951 y Fj(p)1242 3986 y FE(\)\)\()p Fu(context)p FE(\()p Fw(T)1688 3951 y Fj(p)1726 3986 y FE(\))18 b Fv(\000)g Fu(context)p FE(\()p Fw(T)12 b FE(\)\))2273 3951 y Fq(#)868 4041 y Fs(|)p 905 4041 658 10 v 658 w({z)p 1637 4041 V 658 w(})778 4142 y FE(\(no.)37 b(non{cac)n(hed)26 b Fw(T)1464 4112 y Fj(p)1501 4142 y FE({t)n(yp)r(es)h(consisten)n(t)g (with)h Ft(y)q FE(\))2972 3986 y Fu(acpt)o FE(\()p Fw(T)3214 3951 y Fj(p)3252 3986 y FE(\))2972 4041 y Fs(|)p 3009 4041 82 10 v 82 w({z)p 3165 4041 V 82 w(})2435 4142 y FE(\(no.)37 b(calls)27 b(in)h Fw(T)12 b FE({t)n(yp)r(e)26 b Ft(y)k FE(eac)n(h)c(generates\))630 4279 y(=)83 b(\()p Fu(context)o FE(\()p Fw(T)1159 4245 y Fj(p)1197 4279 y FE(\))19 b Fv(\000)f Fu(context)o FE(\()p Fw(T)12 b FE(\)\))1744 4245 y Fq(#)1817 4279 y FE([)p Fu(cf)6 b FE(\()p Fw(T)2001 4245 y Fj(p)2039 4279 y FE(\))18 b(+)g(\(1)h Fv(\000)f Fu(cf)6 b FE(\()p Fw(T)2509 4245 y Fj(p)2546 4279 y FE(\)\))p Fu(acpt)q FE(\()p Fw(T)2854 4245 y Fj(p)2891 4279 y FE(\)])14 b Fw(:)0 4465 y FE(Hence,)74 4623 y Fu(ave)p FE(\()p Fw(T)e FE(\))82 b(=)h(\()p Fu(context)p FE(\()p Fw(T)926 4589 y Fj(p)963 4623 y FE(\))19 b Fv(\000)f Fu(context)p FE(\()p Fw(T)12 b FE(\)\))1511 4589 y Fq(#)1583 4623 y FE([)p Fu(cf)6 b FE(\()p Fw(T)1767 4589 y Fj(p)1805 4623 y FE(\))19 b(+)f(\(1)g Fv(\000)g Fu(cf)6 b FE(\()p Fw(T)2275 4589 y Fj(p)2313 4623 y FE(\)\))p Fu(acpt)p FE(\()p Fw(T)2620 4589 y Fj(p)2658 4623 y FE(\)])14 b Fu(context)o FE(\()p Fw(T)e FE(\))3108 4589 y Fq(#)396 4747 y FE(=)83 b(\()p Fu(cluster)q FE(\()p Fw(T)897 4713 y Fj(p)935 4747 y FE(\))19 b Fv(\000)f Fu(context)o FE(\()p Fw(T)12 b FE(\)\))1482 4713 y Fq(#)1554 4747 y FE([)q Fu(cf)6 b FE(\()p Fw(T)1739 4713 y Fj(p)1776 4747 y FE(\))19 b(+)f(\(1)g Fv(\000)g Fu(cf)6 b FE(\()p Fw(T)2246 4713 y Fj(p)2284 4747 y FE(\)\))p Fu(acpt)p FE(\()p Fw(T)2591 4713 y Fj(p)2629 4747 y FE(\)])14 b Fu(context)p FE(\()p Fw(T)e FE(\))3080 4713 y Fq(#)3138 4747 y Fw(;)42 b FE(b)n(y)27 b(Lemma)g(1\(b,c\))396 4872 y(=)83 b Fu(cluster)q FE(\()p Fw(T)865 4838 y Fj(p)903 4872 y FE(\))935 4838 y Fq(#)1007 4872 y FE([)p Fu(cf)6 b FE(\()p Fw(T)1191 4838 y Fj(p)1229 4872 y FE(\))19 b(+)f(\(1)g Fv(\000)g Fu(cf)6 b FE(\()p Fw(T)1699 4838 y Fj(p)1737 4872 y FE(\)\))p Fu(acpt)p FE(\()p Fw(T)2044 4838 y Fj(p)2082 4872 y FE(\)])14 b Fw(;)42 b FE(b)n(y)27 b(Lemma)g(1\(b\))396 4996 y(=)83 b Fu(cutset)o FE(\()p Fw(T)845 4962 y Fj(p)883 4996 y FE(\))915 4962 y Fq(#)974 4996 y Fu(context)p FE(\()p Fw(T)1324 4962 y Fj(p)1361 4996 y FE(\))1393 4962 y Fq(#)1466 4996 y FE([)p Fu(cf)6 b FE(\()p Fw(T)1650 4962 y Fj(p)1688 4996 y FE(\))19 b(+)f(\(1)g Fv(\000)g Fu(cf)6 b FE(\()p Fw(T)2158 4962 y Fj(p)2196 4996 y FE(\)\))p Fu(acpt)p FE(\()p Fw(T)2503 4962 y Fj(p)2541 4996 y FE(\)])14 b Fw(;)41 b FE(b)n(y)28 b(Lemma)f(1\(a,b\))396 5121 y(=)83 b Fu(cutset)o FE(\()p Fw(T)845 5087 y Fj(p)883 5121 y FE(\))915 5087 y Fq(#)988 5054 y Fs(\002)1023 5121 y Fu(cf)6 b FE(\()p Fw(T)1184 5087 y Fj(p)1221 5121 y FE(\))p Fu(context)p FE(\()p Fw(T)1603 5087 y Fj(p)1641 5121 y FE(\))1673 5087 y Fq(#)1750 5121 y FE(+)18 b(\(1)g Fv(\000)g Fu(cf)7 b FE(\()p Fw(T)2170 5087 y Fj(p)2207 5121 y FE(\)\))p Fu(acpt)p FE(\()p Fw(T)2514 5087 y Fj(p)2552 5121 y FE(\))p Fu(context)p FE(\()p Fw(T)2934 5087 y Fj(p)2972 5121 y FE(\))3004 5087 y Fq(#)3063 5054 y Fs(\003)396 5258 y FE(=)83 b Fu(cutset)o FE(\()p Fw(T)845 5224 y Fj(p)883 5258 y FE(\))915 5224 y Fq(#)988 5191 y Fs(\002)1023 5258 y Fu(cf)6 b FE(\()p Fw(T)1184 5224 y Fj(p)1221 5258 y FE(\))p Fu(context)p FE(\()p Fw(T)1603 5224 y Fj(p)1641 5258 y FE(\))1673 5224 y Fq(#)1750 5258 y FE(+)18 b(\(1)g Fv(\000)g Fu(cf)7 b FE(\()p Fw(T)2170 5224 y Fj(p)2207 5258 y FE(\)\))p Fu(ave)q FE(\()p Fw(T)2480 5224 y Fj(p)2518 5258 y FE(\))2550 5191 y Fs(\003)2598 5258 y Fw(:)p 2649 5233 48 4 v 2649 5283 4 50 v 2693 5283 V 2649 5286 48 4 v 0 5330 1560 4 v 62 5384 a Fo(14)127 5407 y Fn(In)24 b(algorithm)f Fd(r)o(c1)o Fn(,)g(all)g Fm(T)10 b Fn({t)n(yp)r(es)25 b(are)f(non{cac)n(hed)i(\()p Fk(cf)5 b Fn(\()p Fm(T)10 b Fn(\))21 b(=)e(0\).)32 b(In)24 b Fd(r)o(c2)p Fn(,)f(all)g Fm(T)10 b Fn({t)n(yp)r(es)25 b(are)e(cac)n(hed)j(\()p Fk(cf)5 b Fn(\()p Fm(T)10 b Fn(\))20 b(=)g(1\).)1908 5656 y FE(26)p eop %%Page: 27 27 27 26 bop 0 90 a Fb(Pro)s(of)37 b(of)h(Theorem)f(7)0 243 y FE(That)28 b Fu(cluster)p FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)h Fu(cluster)q FE(\()p Fw(T)973 213 y Fj(p)1011 243 y FE(\))k(=)g Fu(context)o FE(\()p Fw(T)12 b FE(\))28 b(follo)n(ws)e(from)h(Lemma)h(1\(e\).)125 343 y(It)g(also)g(follo)n(ws) g(from)g(the)h(de\014nition)g(of)f(a)h(dtree)f(that)h(the)g(clusters)f (of)g(leaf)h(no)r(des)f(corresp)r(ond)f(to)i(the)g(families)f(of)0 443 y(Ba)n(y)n(esian)e(net)n(w)n(ork.)35 b(Therefore,)26 b(eac)n(h)h(family)h(is)f(con)n(tained)g(in)h(some)f(dtree)h(cluster.) 125 542 y(T)-7 b(o)25 b(pro)n(v)n(e)f(the)i(join)n(tree)f(prop)r(ert)n (y)-7 b(,)25 b(w)n(e)g(will)h(use)f(Lemma)g(2.)36 b(Supp)r(ose)26 b(that)g Fw(L;)14 b(M)33 b FE(and)26 b Fw(N)34 b FE(are)25 b(three)g(no)r(des)g(in)h(dtree)0 642 y Fw(T)12 b FE(.)35 b(Supp)r(ose)25 b(further)h(that)f Fw(L)g FE(is)g(on)g(the)h(path)f (connecting)g Fw(M)34 b FE(and)25 b Fw(N)9 b FE(.)36 b(Let)25 b Fw(X)32 b FE(b)r(e)25 b(a)g(no)r(de)g(in)h Fu(cluster)q FE(\()p Fw(M)9 b FE(\))14 b Fv(\\)g Fu(cluster)q FE(\()p Fw(N)9 b FE(\).)0 742 y(W)-7 b(e)28 b(w)n(an)n(t)f(to)g(sho)n (w)g(that)h Fw(X)34 b FE(b)r(elongs)27 b(to)g Fu(cluster)q FE(\()p Fw(L)p FE(\).)37 b(W)-7 b(e)28 b(consider)f(t)n(w)n(o)g(cases.) 0 957 y Ft(Case:)38 b Fw(M)33 b Ft(is)24 b(an)g(ancestor)h(of)g Fw(N)9 b Ft(.)103 b FE(Then)21 b Fw(L)g FE(is)g(an)g(ancestor)f(of)h Fw(N)9 b FE(.)34 b(Since)22 b Fw(X)29 b Fv(2)23 b Fu(cluster)q FE(\()p Fw(N)9 b FE(\),)23 b(then)f Fw(X)29 b Fv(2)24 b Fu(va)n(rs)p FE(\()p Fw(N)9 b FE(\))21 b(and,)0 1057 y(hence,)h Fw(X)29 b Fv(2)24 b Fu(va)n(rs)p FE(\()p Fw(L)p FE(\).)34 b(Since)21 b Fw(X)29 b Fv(2)24 b Fu(cluster)p FE(\()p Fw(M)9 b FE(\),)23 b(then)d(either)h Fw(X)29 b Fv(2)23 b Fu(cutset)p FE(\()p Fw(M)9 b FE(\))20 b(or)g Fw(X)29 b Fv(2)24 b Fu(context)o FE(\()p Fw(M)9 b FE(\).)35 b(If)21 b Fw(X)29 b Fv(2)23 b Fu(cutset)p FE(\()p Fw(M)9 b FE(\),)0 1156 y(then)34 b Fw(X)k Fv(2)33 b Fu(va)n(rs)p FE(\()p Fw(M)648 1126 y Fj(l)673 1156 y FE(\))h(and)f Fw(X)39 b Fv(2)32 b Fu(va)n(rs)p FE(\()p 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Fu(cluster)q FE(\()p Fw(O)r FE(\))j(\(giv)n(en)0 1671 y(the)k(ab)r(o)n(v)n(e)e(case\).)59 b(Without)36 b(loss)e(of)h(generalit)n(y)-7 b(,)36 b(supp)r(ose)f(that)h Fw(M)44 b FE(is)35 b(in)g(the)h(left)g(subtree)f(of)g Fw(O)j FE(and)d Fw(N)44 b FE(is)35 b(in)h(the)0 1770 y(righ)n(t)30 b(subtree.)47 b(Since)31 b Fw(X)k Fv(2)30 b Fu(va)n(rs)p FE(\()p Fw(M)9 b FE(\),)32 b(then)f Fw(X)k Fv(2)29 b Fu(va)n(rs)q FE(\()p Fw(O)1906 1740 y Fj(l)1932 1770 y FE(\).)47 b(Since)32 b Fw(X)j Fv(2)29 b Fu(va)n(rs)p FE(\()p Fw(N)9 b FE(\),)32 b(then)g Fw(X)j Fv(2)29 b Fu(va)n(rs)p FE(\()p Fw(O)3388 1740 y Fj(r)3426 1770 y FE(\).)47 b(Therefore,)0 1870 y Fw(X)29 b Fv(2)24 b Fu(cluster)q FE(\()p Fw(O)r FE(\))k(b)n(y)g(Lemma)f(2.)p 1066 1845 48 4 v 1066 1895 4 50 v 1110 1895 V 1066 1898 48 4 v 0 2102 a Fb(Pro)s(of)37 b(of)h(Theorem)f(8)0 2255 y FE(W)-7 b(e)28 b(need)g(a)f(couple)g(of)h(lemmas)f(\014rst.)0 2436 y Ft(Lemma)j(3)41 b Fx(When)22 b(pr)l(o)l(c)l(essing)g(variable)i Fw(\031)s FE(\()p Fw(i)p FE(\))e Fx(in)g Ff(el2dt)o Fx(,)i(the)e (cluster)f(of)i(any)f(no)l(de)g Fw(N)30 b Fx(which)23 b(is)f(adde)l(d)i(in)d(the)h(pr)l(o)l(c)l(ess)g(of)0 2536 y(c)l(omp)l(osing)j(tr)l(e)l(es)e Fw(T)630 2548 y Fq(1)667 2536 y Fw(;)14 b(:)g(:)g(:)f(;)h(T)900 2548 y Fj(n)969 2536 y Fx(must)22 b(b)l(e)i(include)l(d)h(in)e Fu(va)n(rs)q FE(\()p Fw(T)12 b FE(\))5 b Fv(\\)g(f)p Fw(\031)s FE(\()p Fw(i)p FE(\))p Fw(;)14 b(:)g(:)g(:)g(;)g(\031)s FE(\()p Fw(n)p FE(\))p Fv(g)p Fx(,)25 b(wher)l(e)g Fw(T)34 b FE(=)22 b Ff(compose)q FE(\()p Fw(T)3457 2548 y Fq(1)3494 2536 y Fw(;)14 b(:)g(:)g(:)f(;)h(T)3727 2548 y Fj(n)3772 2536 y FE(\))p Fx(.)3829 2506 y Fq(15)0 2717 y FE(Supp)r(ose)28 b(that)g(a)f(v)-5 b(ariable)27 b Fw(X)34 b FE(b)r(elongs)27 b(to)h Fu(cluster)q FE(\()p Fw(N)9 b FE(\).)37 b(Then,)29 b(b)n(y)e(Lemma)h(2,)f Fw(X)34 b FE(m)n(ust)28 b(either)g(b)r(elong)f (to)h(t)n(w)n(o)f(trees)g(in)0 2817 y Fw(T)49 2829 y Fq(1)86 2817 y Fw(;)14 b(:)g(:)g(:)f(;)h(T)319 2829 y Fj(n)364 2817 y FE(,)28 b(or)f(b)r(elong)h(to)g(a)g(tree)g(in)g Fw(T)1268 2829 y Fq(1)1305 2817 y Fw(;)14 b(:)g(:)g(:)f(;)h(T)1538 2829 y Fj(n)1611 2817 y FE(and)28 b(another)f(tree)h(in)g(\006)19 b Fv(\000)f(f)p Fw(T)2595 2829 y Fq(1)2631 2817 y Fw(;)c(:)g(:)g(:)g(;) g(T)2865 2829 y Fj(n)2910 2817 y Fv(g)p FE(.)38 b(In)28 b(either)g(case,)f Fw(X)35 b FE(cannot)0 2916 y(b)r(elong)27 b(to)g Fv(f)p Fw(\031)s FE(\(1\))p Fw(;)14 b(:)g(:)g(:)g(;)g(\031)s FE(\()p Fw(i)k Fv(\000)g FE(1\))p Fv(g)27 b FE(since)g(these)g(v)-5 b(ariables)26 b(ha)n(v)n(e)h(already)f(b)r(een)h(pro)r(cessed,)g(so)f (eac)n(h)h(can)g(b)r(elong)g(only)g(to)0 3016 y(a)32 b(single)g(tree)g(in)g(\006.)51 b(Therefore,)33 b Fw(X)38 b FE(m)n(ust)33 b(b)r(elong)f(to)g Fw(\031)s FE(\()p Fw(i)p FE(\))p Fw(;)14 b(:)g(:)g(:)g(;)g(\031)s FE(\()p Fw(n)p FE(\).)51 b(Moreo)n(v)n(er,)31 b Fw(X)39 b FE(m)n(ust)32 b(b)r(elong)g(to)g(at)h(least)e(one)0 3116 y(tree)c(in)h Fw(T)312 3128 y Fq(1)349 3116 y Fw(;)14 b(:)g(:)g(:)f(;)h(T)582 3128 y Fj(n)627 3116 y FE(.)37 b(Hence,)28 b Fw(X)34 b FE(m)n(ust)28 b(b)r(elong)f(to)g Fw(T)39 b FE(and)27 b Fw(X)j Fv(2)23 b Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)h(f)p Fw(\031)s FE(\()p Fw(i)p FE(\))p Fw(;)14 b(:)g(:)g(:)g(;)g(\031)s FE(\()p Fw(n)p FE(\))p Fv(g)p FE(.)p 3038 3091 V 3038 3141 4 50 v 3081 3141 V 3038 3144 48 4 v 0 3297 a Ft(Lemma)30 b(4)41 b Fx(L)l(et)27 b FE(\000)h Fx(b)l(e)f(a)i(c)l(ol)t(le)l(ction)g(of)f(sets)g Fw(S)1492 3309 y Fq(1)1529 3297 y Fw(;)14 b(:)g(:)g(:)f(;)h(S)1764 3309 y Fj(n)1809 3297 y Fx(,)29 b(wher)l(e)f Fw(S)2146 3309 y Fj(i)2201 3297 y Fx(is)h(the)e(family)j(of)e(variable)i Fw(\031)s FE(\()p Fw(i)p FE(\))e Fx(in)g(network)g Fv(N)12 b Fx(.)39 b(T)-6 b(o)0 3396 y(eliminate)31 b(variable)g Fw(\031)s FE(\()p Fw(i)p FE(\))f Fx(fr)l(om)g FE(\000)g Fx(is)g(to)f(r)l(eplac)l(e)i(the)e(sets)h Fw(S)1941 3408 y Fj(k)2011 3396 y Fx(c)l(ontaining)g Fw(\031)s FE(\()p Fw(i)p FE(\))g Fx(by)g(the)g(set)f FE(\()2996 3334 y Fs(S)3065 3421 y Fj(k)3120 3396 y Fw(S)3171 3408 y Fj(k)3212 3396 y FE(\))18 b Fv(\000)g(f)p Fw(\031)s FE(\()p Fw(i)p FE(\))p Fv(g)p Fx(.)38 b(Now,)30 b(if)0 3496 y(we)d(start)f (eliminating)i(variables)h(ac)l(c)l(or)l(ding)f(to)f(the)g(or)l(der)g Fw(\031)s Fx(,)h(c)l(oncurr)l(ently,)g(fr)l(om)f(the)g(mor)l(al)g(gr)l (aph)h Fw(G)f Fx(of)h Fv(N)39 b Fx(and)27 b(fr)l(om)0 3596 y(the)k(c)l(ol)t(le)l(ction)h FE(\000)p Fx(,)f(we)g(\014nd)f(the)h (fol)t(lowing.)43 b(As)31 b(we)g(ar)l(e)f(ab)l(out)h(to)g(eliminate)g (variable)i Fw(\031)s FE(\()p Fw(i)p FE(\))p Fx(,)f(the)e(set)h FE(\()3323 3533 y Fs(S)3392 3621 y Fj(k)3447 3596 y Fw(S)3498 3608 y Fj(k)3539 3596 y FE(\))19 b Fv(\000)f(f)p Fw(\031)s FE(\()p Fw(i)p FE(\))p Fv(g)0 3695 y Fx(wil)t(l)31 b(c)l(ontain)f (exactly)g(the)g(neighb)l(ors)h(of)g Fw(\031)s FE(\()p Fw(i)p FE(\))f Fx(in)g(gr)l(aph)h Fw(G)p Fx(.)0 3876 y FE(It)d(su\016ces)g(to)f(sho)n(w)g(that)i(t)n(w)n(o)e(no)r(des)g(app) r(ear)g(in)h(the)g(same)g(set)g(in)g(\000)g(i\013)g(they)g(are)f (connected)h(b)n(y)f(an)h(edge)f(in)h Fw(G)p FE(.)38 b(This)0 3976 y(follo)n(ws)23 b(initially)-7 b(,)25 b(b)r(efore)f(an)n (y)f(v)-5 b(ariable)23 b(is)h(eliminated.)36 b(Moreo)n(v)n(er,)22 b(it)i(is)g(easy)f(to)h(sho)n(w)f(that)h(it)g(con)n(tin)n(ues)g(to)g (hold)f(after)0 4076 y(a)k(v)-5 b(ariable)27 b(has)g(b)r(een)h (eliminated.)p 1154 4051 V 1154 4101 4 50 v 1198 4101 V 1154 4104 48 4 v 125 4175 a(No)n(w)34 b(algorithm)f Ff(el2dt)p FE(\()p Fv(N)12 b Fw(;)i(\031)s FE(\))35 b(can)g(b)r(e)g (view)n(ed)f(as)g(p)r(erforming)f(v)-5 b(ariable)34 b(elimination)g(on) h(a)f(collection)g(of)g(sets,)0 4275 y(whic)n(h)c(initially)g(con)n (tains)f(the)h(families)g(of)g Fv(N)12 b FE(.)44 b(W)-7 b(e)31 b(need)f(to)g(establish)f(this)h(corresp)r(ondence)e(\014rst)i (in)g(order)f(to)h(pro)n(v)n(e)0 4374 y(our)f(theorem.)43 b(After)30 b(pro)r(cessing)f(v)-5 b(ariable)29 b Fw(\031)s FE(\()p Fw(i)p FE(\))h(in)g(algorithm)f Ff(el2dt)o FE(,)i(the)f(set)g (of)g(v)-5 b(ariables)28 b(represen)n(ted)h(b)n(y)g(tree)h Fw(T)0 4474 y FE(in)e(\006)f(is)1204 4582 y Fu(set)o FE(\()p Fw(T)12 b FE(\))1464 4531 y Fe(def)1482 4582 y FE(=)55 b Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)h(f)p Fw(\031)s FE(\()p Fw(i)f FE(+)g(1\))p Fw(;)c(:)g(:)g(:)f(;) h(\031)s FE(\()p Fw(n)p FE(\))p Fv(g)p FE(;)0 4731 y(that)28 b(is,)f(v)-5 b(ariables)27 b(in)h Fw(T)38 b FE(that)28 b(ha)n(v)n(e)f(not)g(b)r(een)h(pro)r(cessed)f(y)n(et.)125 4830 y(Initially)-7 b(,)38 b(the)e(trees)f(in)i(\006)f(represen)n(t)e (the)j(families)e(in)i Fv(N)12 b FE(.)62 b(As)36 b(w)n(e)g(pro)r(cess)e (v)-5 b(ariable)35 b Fw(\031)s FE(\()p Fw(i)p FE(\),)k(w)n(e)c(collect) h(all)g(trees)0 4930 y Fw(T)49 4942 y Fq(1)86 4930 y Fw(;)14 b(:)g(:)g(:)f(;)h(T)319 4942 y Fj(n)404 4930 y FE(suc)n(h)39 b(that)i Fw(\031)s FE(\()p Fw(i)p FE(\))j Fv(2)f Fu(set)p FE(\()p Fw(T)1261 4942 y Fq(1)1298 4930 y FE(\))p Fw(;)14 b(:)g(:)g(:)g(;)g Fu(set)p FE(\()p Fw(T)1695 4942 y Fj(n)1740 4930 y FE(\))40 b(and)g(replace)e(them)j(b)n (y)e(the)i(tree)e Ff(compose)p FE(\()p Fw(T)3393 4942 y Fq(1)3430 4930 y Fw(;)14 b(:)g(:)g(:)g(;)g(T)3664 4942 y Fj(n)3709 4930 y FE(\).)74 b(It)0 5029 y(follo)n(ws)27 b(that)856 5129 y Fu(set)p FE(\()p Ff(compose)p FE(\()p Fw(T)1415 5141 y Fq(1)1452 5129 y Fw(;)14 b(:)g(:)g(:)g(;)g(T)1686 5141 y Fj(n)1730 5129 y FE(\)\))24 b(=)f Fu(set)o FE(\()p Fw(T)2085 5141 y Fq(1)2122 5129 y FE(\))c Fv([)g Fw(:)14 b(:)g(:)k Fv([)h Fu(set)p FE(\()p Fw(T)2616 5141 y Fj(n)2661 5129 y FE(\))f Fv(\000)h(f)p Fw(\031)s FE(\()p Fw(i)p FE(\))p Fv(g)p Fw(;)0 5278 y FE(and)27 b(hence)h(the)g(corresp)r (ondence)e(w)n(e)h(are)g(seeking.)p 0 5330 1560 4 v 62 5384 a Fo(15)127 5407 y Fn(W)-6 b(e)24 b(are)g(referring)f(to)h(the)g (cluster)g(of)g Fm(N)30 b Fn(in)24 b(the)g(\014nal)g(dtree)g(returned)h (b)n(y)f Fd(el2dt)p Fn(.)1908 5656 y FE(27)p eop %%Page: 28 28 28 27 bop 125 90 a FE(F)-7 b(rom)40 b(this)h(corresp)r(ondence,)h(and)f (Lemma)g(4,)i(w)n(e)e(conclude)f(that)h(when)g(pro)r(cessing)f(v)-5 b(ariable)39 b Fw(\031)s FE(\()p Fw(i)p FE(\),)45 b(the)c(tree)0 190 y Fw(T)34 b FE(=)23 b Ff(compose)p FE(\()p Fw(T)599 202 y Fq(1)636 190 y Fw(;)14 b(:)g(:)g(:)g(;)g(T)870 202 y Fj(n)914 190 y FE(\),)24 b(whic)n(h)d(is)h(added)g(to)g(\006,)h (is)e(suc)n(h)h(that)g Fu(set)p FE(\()p Fw(T)12 b FE(\))21 b(con)n(tains)g(exactly)h(the)g(neigh)n(b)r(ors)e(of)i(v)-5 b(ariable)0 289 y Fw(\031)s FE(\()p Fw(i)p FE(\))28 b(in)f(the)h(moral) e(graph)g Fw(G)h FE(of)g Fv(N)40 b FE(after)27 b(ha)n(ving)f (eliminated)h Fw(\031)s FE(\(1\))p Fw(;)14 b(:)g(:)g(:)g(;)g(\031)s FE(\()p Fw(i)k Fv(\000)f FE(1\))27 b(from)g(it.)37 b(This)27 b(means)f(that)i(the)f(size)0 389 y(of)h Fu(set)p FE(\()p Fw(T)12 b FE(\))24 b(=)g Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))18 b Fv(\\)i(f)p Fw(\031)s FE(\()p Fw(i)e FE(+)h(1\))p Fw(;)14 b(:)g(:)g(:)f(;)h(\031)s FE(\()p Fw(n)p FE(\))p Fv(g)29 b FE(is)f Fv(\024)c Fx(width)7 b FE(\()p Fw(\031)s FE(\))29 b(and,)g(hence,)f(the)h(size)f(of)g Fu(va)n(rs)p FE(\()p Fw(T)12 b FE(\))19 b Fv(\\)g(f)p Fw(\031)s FE(\()p Fw(i)p FE(\))p Fw(;)14 b(:)g(:)g(:)g(;)g(\031)s FE(\()p Fw(n)p FE(\))p Fv(g)28 b FE(is)0 489 y Fv(\024)23 b Fx(width)7 b FE(\()p Fw(\031)s FE(\))19 b(+)f(1.)125 588 y(Giv)n(en)h(Lemma)h(3,)h (this)f(means)f(that)h(the)g(cluster)f(of)h(an)n(y)f(no)r(de)h(whic)n (h)f(is)h(added)g(as)f(a)g(result)h(of)f(comp)r(osing)g Fw(T)3585 600 y Fq(1)3622 588 y Fw(;)14 b(:)g(:)g(:)f(;)h(T)3855 600 y Fj(n)0 688 y FE(cannot)31 b(b)r(e)h(bigger)e(than)i Fx(width)7 b FE(\()p Fw(\031)s FE(\))22 b(+)f(1.)48 b(This)32 b(pro)n(v)n(es)d(that)j(the)g(width)g(of)f(constructed)g(dtree)h(is)f (no)g(more)g(than)h(the)0 788 y(width)c(of)g(order)e Fw(\031)s FE(.)p 648 763 48 4 v 648 812 4 50 v 692 812 V 648 815 48 4 v 0 1019 a Fb(Pro)s(of)37 b(of)h(Theorem)f(9)0 1173 y FE(That)g Ff(bal-dt)p FE(\()p Fw(T)12 b FE(\))37 b(tak)n(es)f Fw(O)r FE(\()p Fw(n)14 b FE(log)h Fw(n)p FE(\))37 b(time)h(and)f(returns)g(a)g(binary)f(tree)h(of)g(heigh)n(t)g Fw(O)r FE(\(log)15 b Fw(n)p FE(\))38 b(follo)n(ws)e(immediately)0 1272 y(from)31 b(the)h(prop)r(erties)e(of)i(the)f Ff(contra)n(ct)h FE(op)r(eration)e([24)o(].)48 b(That)32 b Ff(bal-dt)p FE(\()p Fw(T)12 b FE(\))31 b(is)g(a)g(dtree)g(follo)n(ws)g(from)g(the)g (w)n(a)n(y)f(w)n(e)0 1372 y(initialized)e(the)g(lab)r(els)f(of)h(no)r (des)f(in)h Fw(T)12 b FE(.)125 1471 y(T)-7 b(o)36 b(pro)n(v)n(e)g(the)i (results)e(on)h(widths,)j(w)n(e)d(need)g(to)h(in)n(tro)r(duce)e(some)h (new)g(notation.)66 b(Since)37 b(the)h(call)e Ff(bal-dt)p FE(\()p Fw(T)12 b FE(\))0 1571 y(mo)r(di\014es)34 b(dtree)g Fw(T)45 b FE(using)34 b(the)g Ff(contra)n(ct)g FE(op)r(eration,)h(w)n (e)f(will)g(use)g Fw(T)2345 1583 y Fq(0)2382 1571 y Fw(;)14 b(T)2468 1583 y Fq(1)2504 1571 y Fw(;)g(T)2590 1583 y Fq(2)2627 1571 y Fw(;)g(:)g(:)g(:)p FE(,)36 b(where)d Fw(T)3115 1583 y Fq(0)3186 1571 y FE(=)g Fw(T)12 b FE(,)35 b(to)f(denote)g(the)0 1671 y(mo)r(di\014ed)g(dtrees)f(after)g(eac)n(h)g Ff(rake)h FE(or)e Ff(compress)i FE(op)r(eration.)54 b(Moreo)n(v)n(er,) 33 b(w)n(e)g(will)h(use)f Fw(N)3073 1683 y Fj(i)3134 1671 y FE(to)g(denote)h(no)r(de)f Fw(N)43 b FE(in)0 1770 y(dtree)27 b Fw(T)261 1782 y Fj(i)289 1770 y FE(.)125 1870 y(W)-7 b(e)20 b(will)f(use)h Fx(Lvars)7 b FE(\()p Fw(N)i FE(\))20 b(to)g(denote)f(the)h(v)-5 b(ariables)19 b(app)r(earing)f(in)i(dtree)f Ff(label)p FE(\()p Fw(N)9 b FE(\);)23 b Fx(Lvars)3032 1834 y Fp(#)3070 1870 y FE(\()p Fw(N)9 b FE(\))20 b(to)g(denote)f(v)-5 b(ariables)0 1970 y(app)r(earing)30 b(in)i(dtrees)f Ff(label)p FE(\()p Fw(M)9 b FE(\),)32 b(where)f Fw(M)38 b FE(=)30 b Fw(N)40 b FE(or)30 b Fw(M)41 b FE(is)31 b(a)g(descenden)n(t)g(of)h Fw(N)9 b FE(;)33 b Fx(Lvars)2997 1933 y Fp(")3035 1970 y FE(\()p Fw(N)9 b FE(\))32 b(to)f(denote)g(v)-5 b(ariables)0 2069 y(app)r(earing)26 b(in)i(dtrees)f Ff(label)p FE(\()p Fw(M)9 b FE(\),)28 b(where)f Fw(M)36 b FE(is)28 b(connected)f(to)h Fw(N)36 b FE(through)27 b(its)h(paren)n(t.)125 2169 y(W)-7 b(e)28 b(\014rst)f(pro)n(v)n(e)f(t)n(w)n(o)h(lemmas.)0 2348 y Ft(Lemma)j(5)41 b Fx(We)30 b(have)h Fv(j)23 b Fx(Lvars)1024 2311 y Fp(#)1062 2348 y FE(\()p Fw(N)1161 2360 y Fj(i)1189 2348 y FE(\))c Fv(\\)f Fx(Lvars)1522 2311 y Fp(")1560 2348 y FE(\()p Fw(N)1659 2360 y Fj(i)1687 2348 y FE(\))23 b Fv(j\024)g Fw(w)r Fx(.)0 2526 y FE(This)k(holds)g(in) g Fw(T)551 2538 y Fq(0)615 2526 y FE(since)g Fx(Lvars)1027 2490 y Fp(#)1065 2526 y FE(\()p Fw(N)1164 2538 y Fq(0)1201 2526 y FE(\))18 b Fv(\\)g Fx(Lvars)1532 2490 y Fp(")1570 2526 y FE(\()p Fw(N)1669 2538 y Fq(0)1707 2526 y FE(\))23 b(=)g Fu(context)o FE(\()p Fw(N)2205 2538 y Fq(0)2242 2526 y FE(\))28 b(b)n(y)f(Lemma)g(2,)f(whic)n(h)h(size)g(is)g Fv(\024)c Fw(w)r FE(.)37 b(W)-7 b(e)28 b(need)f(to)0 2626 y(pro)n(v)n(e)f(that)i(the)g Ff(rake)f FE(and)h Ff(compress)g FE(op)r(erations)e(preserv)n(e)g(this)i(in)n(v)-5 b(arian)n(t.)125 2789 y Fv(\017)41 b Ff(compress)p FE(:)58 b(after)38 b(absorbing)e Fw(N)1334 2801 y Fj(i)1361 2753 y(p)1438 2789 y FE(in)n(to)i Fw(N)1684 2801 y Fj(i)1749 2789 y FE(to)g(yield)g Fw(N)2139 2801 y Fj(i)p Fq(+1)2251 2789 y FE(,)i(w)n(e)e(ha)n(v)n(e)f Fx(Lvars)2857 2753 y Fp(#)2896 2789 y FE(\()p Fw(N)2995 2801 y Fj(i)p Fq(+1)3106 2789 y FE(\))k(=)f Fx(Lvars)3493 2753 y Fp(#)3531 2789 y FE(\()p Fw(N)3630 2801 y Fj(i)3657 2753 y(p)3696 2789 y FE(\))e(and)208 2888 y Fx(Lvars)416 2852 y Fp(")454 2888 y FE(\()p Fw(N)553 2900 y Fj(i)p Fq(+1)665 2888 y FE(\))26 b(=)g Fx(Lvars)1023 2852 y Fp(")1061 2888 y FE(\()p Fw(N)1160 2900 y Fj(i)1188 2852 y(p)1226 2888 y FE(\).)43 b(Therefore,)29 b Fx(Lvars)1934 2852 y Fp(#)1973 2888 y FE(\()p Fw(N)2072 2900 y Fj(i)p Fq(+1)2183 2888 y FE(\))20 b Fv(\\)g Fx(Lvars)2519 2852 y Fp(")2557 2888 y FE(\()p Fw(N)2656 2900 y Fj(i)p Fq(+1)2768 2888 y FE(\))26 b(=)g Fx(Lvars)3126 2852 y Fp(#)3164 2888 y FE(\()p Fw(N)3263 2900 y Fj(i)3291 2852 y(p)3329 2888 y FE(\))20 b Fv(\\)g Fx(Lvars)3665 2852 y Fp(")3703 2888 y FE(\()p Fw(N)3802 2900 y Fj(i)3829 2852 y(p)3868 2888 y FE(\))208 2988 y(and)27 b(the)h(in)n(v)-5 b(arian)n(t)26 b(holds)i(in)g Fw(T)1224 3000 y Fj(i)p Fq(+1)1362 2988 y FE(giv)n(en)f(that)h(it)g (holds)f(in)h Fw(T)2205 3000 y Fj(i)2232 2988 y FE(.)125 3152 y Fv(\017)41 b Ff(rake)p FE(:)62 b(after)40 b(absorbing)f(the)i(c) n(hildren)f Fw(N)1646 3164 y Fj(i)1674 3116 y(l)1740 3152 y FE(and)g Fw(N)1981 3164 y Fj(i)2008 3116 y(r)2086 3152 y FE(in)n(to)g Fw(N)2334 3164 y Fj(i)2402 3152 y FE(to)g(yield)h Fw(N)2797 3164 y Fj(i)p Fq(+1)2908 3152 y FE(,)j Ff(label)p FE(\()p Fw(N)3305 3164 y Fj(i)p Fq(+1)3416 3152 y FE(\))d(will)g(b)r(e)g(the)208 3252 y(comp)r(osition)29 b(of)h Ff(label)p FE(\()p Fw(N)1101 3264 y Fj(i)1129 3252 y FE(\),)h Ff(label)p FE(\()p Fw(N)1545 3264 y Fj(i)1572 3216 y(l)1598 3252 y FE(\))f(and)g Ff(label)p FE(\()p Fw(N)2154 3264 y Fj(i)2182 3216 y(r)2218 3252 y FE(\).)46 b(Therefore,)29 b Fx(Lvars)2930 3216 y Fp(#)2968 3252 y FE(\()p Fw(N)3067 3264 y Fj(i)p Fq(+1)3179 3252 y FE(\))e(=)g Fx(Lvars)3539 3216 y Fp(#)3577 3252 y FE(\()p Fw(N)3676 3264 y Fj(i)3704 3252 y FE(\))j(and)208 3352 y Fx(Lvars)416 3316 y Fp(")454 3352 y FE(\()p 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b(construction,)h Ff(label)p FE(\()p Fw(N)1325 3821 y Fq(0)1362 3809 y FE(\))g(m)n(ust)h(b)r(e)f(the)h(empt)n(y)f (dtree.)37 b(Supp)r(ose)27 b(that)g Ff(label)p FE(\()p Fw(N)3214 3821 y Fj(i)3242 3809 y FE(\))g(is)g(not)g(the)h(empt)n(y)0 3908 y(dtree.)50 b(Then)33 b(a)e(no)r(de)i(m)n(ust)f(ha)n(v)n(e)f(b)r (een)h(absorb)r(ed)f(in)n(to)h Fw(N)41 b FE(in)33 b(some)e(dtree)h Fw(T)2584 3920 y Fq(0)2621 3908 y Fw(;)14 b(:)g(:)g(:)g(;)g(T)2855 3920 y Fj(i)2882 3908 y FE(.)50 b(This)32 b(is)g(imp)r(ossible)g (though)0 4008 y(since)d Fw(N)39 b FE(cannot)29 b(b)r(e)h(part)f(of)h (an)n(y)f(c)n(hain)g(in)h(these)g(dtrees,)f(and)h Fw(N)38 b FE(is)30 b(not)g(a)f(leaf)g(in)h(an)n(y)f(of)h(these)g(dtrees.)42 b(Therefore,)0 4108 y(neither)28 b Ff(compress)g FE(nor)f Ff(rake)g FE(could)h(ha)n(v)n(e)e(altered)h(the)h(lab)r(el)g(of)f Fw(N)37 b FE(in)27 b(dtrees)h Fw(T)2690 4120 y Fq(0)2726 4108 y Fw(;)14 b(:)g(:)g(:)g(;)g(T)2960 4120 y Fj(i)2987 4108 y FE(.)p 3038 4083 V 3038 4133 4 50 v 3082 4133 V 3038 4136 48 4 v 125 4207 a(W)-7 b(e)29 b(no)n(w)f(pro)r(ceed)g(to)h (pro)n(v)n(e)e(the)i(rest)f(of)h(this)g(theorem.)40 b(Initially)-7 b(,)30 b(the)f(dtrees)f(in)h(the)h(lab)r(els)e(of)h Fw(T)3348 4219 y Fq(0)3414 4207 y FE(represen)n(t)e(leaf)0 4307 y(no)r(des)j(in)g(the)g(\014nal)g(dtree)f(returned)h(b)n(y)f Ff(bal-dt)p FE(.)44 b(Since)30 b(these)g(no)r(des)g(are)e(lea)n(v)n (es,)h(they)h(do)g(not)g(ha)n(v)n(e)e(cutsets.)44 b(That)0 4407 y(the)34 b(con)n(text)f(and)h(cluster)f(sizes)g(of)h(these)g(no)r (des)f(ha)n(v)n(e)g(the)h(claimed)f(sizes)g(in)h(the)g(\014nal)g(dtree) f(returned)h(b)n(y)f Ff(bal-dt)0 4506 y FE(follo)n(ws)27 b(immediately)g(from)h(the)g(fact)f(that)h(they)g(corresp)r(ond)e(to)h (the)h(lea)n(v)n(es)e(in)i(dtree)g Fw(T)2879 4518 y Fq(0)2915 4506 y FE(.)125 4606 y(There)j(are)h(three)g(w)n(a)n(ys)f(in)h(whic)n (h)g Ff(compose)h FE(can)f(add)g(a)g(new)g(dtree)g(no)r(de)h Fw(d)f FE(to)h(com)n(bine)f(t)n(w)n(o)f(dtrees)h(together.)0 4705 y(W)-7 b(e)25 b(will)f(sho)n(w)g(that)g(the)h(cutset,)g(con)n (text)f(and)g(cluster)g(of)h(eac)n(h)e(added)h(no)r(de)h Fw(d)f FE(will)h(ha)n(v)n(e)e(the)i(claimed)f(size)g(in)g(the)h (\014nal)0 4805 y(dtree)30 b(returned)f(b)n(y)g Ff(bal-dt)p FE(.)44 b(In)30 b(what)g(follo)n(ws,)f Fu(cutset)o FE(\()p Fw(d)p FE(\),)j Fu(context)o FE(\()p Fw(d)p FE(\))f(and)e Fu(cluster)q FE(\()p Fw(d)p FE(\))i(refer)e(to)h(the)g(cutset,)g(con)n (text)0 4905 y(and)d(cluster)h(of)f(no)r(de)h Fw(d)g FE(in)g(the)g(\014nal)f(dtree)g(returned)h(b)n(y)f Ff(bal-dt)p FE(.)125 5004 y Ft(Case)i(1.)36 b FE(W)-7 b(e)26 b(ha)n(v)n(e)e(a)h(c)n (hain)h Fw(N)1144 5016 y Fj(i)1186 5004 y Fv(\000)14 b Fw(O)1328 5016 y Fj(i)1371 5004 y Fv(\000)g Fw(P)1503 5016 y Fj(i)1531 5004 y FE(,)26 b(where)f Fw(N)1885 5016 y Fj(i)1938 5004 y FE(is)h(absorb)r(ed)f(in)n(to)g(c)n(hild)h Fw(O)2800 5016 y Fj(i)2854 5004 y FE(b)n(y)f Ff(compress)p FE(,)i(creating)d(dtree)0 5104 y Fw(d)f FE(=)g Ff(label)p FE(\()p Fw(O)480 5116 y Fj(i)p Fq(+1)592 5104 y FE(\))g(=)g Ff(compose)p FE(\()p Ff(label)p FE(\()p Fw(N)1444 5116 y Fj(i)1472 5104 y FE(\))p Fw(;)14 b Ff(label)o FE(\()p Fw(O)1866 5116 y Fj(i)1895 5104 y FE(\)\).)37 b(Then)1217 5283 y Fu(cutset)o FE(\()p Fw(d)p FE(\))84 b Fv(\022)f Fx(Lvars)7 b FE(\()p Fw(N)2071 5295 y Fj(i)2099 5283 y FE(\))18 b Fv(\\)h Fx(Lvars)8 b FE(\()p Fw(O)2527 5295 y Fj(i)2555 5283 y FE(\))1616 5407 y Fv(\022)83 b Fx(Lvars)1972 5371 y Fp(")2010 5407 y FE(\()p Fw(O)2105 5419 y Fj(i)2133 5407 y FE(\))19 b Fv(\\)g Fx(Lvars)2466 5371 y Fp(#)2505 5407 y FE(\()p Fw(O)2600 5419 y Fj(i)2628 5407 y FE(\))p Fw(;)1908 5656 y FE(28)p eop %%Page: 29 29 29 28 bop 0 90 a FE(whic)n(h)28 b(size)f(is)g Fv(\024)c Fw(w)30 b FE(b)n(y)e(Lemma)f(5.)36 b(Moreo)n(v)n(er,)25 b(b)n(y)j(Lemma)f(2,)640 280 y Fu(context)p FE(\()p Fw(d)p FE(\))84 b(=)e(\()p Fx(Lvars)8 b FE(\()p Fw(N)1575 292 y Fj(i)1603 280 y FE(\))18 b Fv([)h Fx(Lvars)8 b FE(\()p Fw(O)2031 292 y Fj(i)2059 280 y FE(\)\))19 b Fv(\\)2390 201 y Fs([)2216 379 y Fj(K)2272 387 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Fw(N)742 798 y Fj(i)794 786 y FE(has)e(a)h(single)f(c)n(hild)h Fw(O)1495 798 y Fj(i)1523 786 y FE(,)h(where)f Fw(O)1873 798 y Fj(i)1926 786 y FE(is)f(a)h(leaf.)36 b(No)r(de)25 b Fw(O)2536 798 y Fj(i)2589 786 y FE(is)g(absorb)r(ed)f(in)n(to)h (paren)n(t)f Fw(N)3512 798 y Fj(i)3564 786 y FE(b)n(y)h Ff(rake)p FE(,)0 885 y(creating)h(dtree)i Fw(d)23 b FE(=)g Ff(label)o FE(\()p Fw(N)1014 897 y Fj(i)p Fq(+1)1126 885 y FE(\))g(=)g Ff(compose)p FE(\()p Ff(label)p FE(\()p Fw(N)1978 897 y Fj(i)2006 885 y FE(\))p Fw(;)14 b Ff(label)p FE(\()p Fw(O)2401 897 y Fj(i)2429 885 y FE(\)\).)37 b(W)-7 b(e)28 b(ha)n(v)n(e)1217 1063 y Fu(cutset)o FE(\()p Fw(d)p FE(\))84 b Fv(\022)f Fx(Lvars)7 b FE(\()p Fw(N)2071 1075 y Fj(i)2099 1063 y FE(\))18 b Fv(\\)h Fx(Lvars)8 b FE(\()p Fw(O)2527 1075 y Fj(i)2555 1063 y FE(\))1616 1187 y Fv(\022)83 b Fx(Lvars)1972 1151 y Fp(")2010 1187 y FE(\()p Fw(O)2105 1199 y Fj(i)2133 1187 y FE(\))19 b Fv(\\)g Fx(Lvars)2466 1151 y Fp(#)2505 1187 y FE(\()p Fw(O)2600 1199 y Fj(i)2628 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b Fv(\022)f Fx(Lvars)7 b FE(\()p Fw(O)2067 2449 y Fj(i)2095 2437 y FE(\))19 b Fv(\\)g Fx(Lvars)7 b FE(\()p Fw(P)2513 2449 y Fj(i)2542 2437 y FE(\))1616 2562 y Fv(\022)83 b Fx(Lvars)1972 2525 y Fp(")2010 2562 y FE(\()p Fw(O)2105 2574 y Fj(i)2133 2562 y FE(\))19 b Fv(\\)g Fx(Lvars)2466 2525 y Fp(#)2505 2562 y FE(\()p Fw(O)2600 2574 y Fj(i)2628 2562 y FE(\))p Fw(;)0 2739 y FE(whic)n(h)28 b(size)f(is)g Fv(\024)c Fw(w)r FE(.)38 b(Moreo)n(v)n(er,)761 2928 y Fu(context)o FE(\()p Fw(d)p FE(\))84 b(=)f(\()p Fx(Lvars)8 b FE(\()p Fw(O)1692 2940 y Fj(i)1720 2928 y FE(\))19 b Fv([)f Fx(Lvars)8 b FE(\()p Fw(P)2138 2940 y Fj(i)2166 2928 y FE(\)\))19 b Fv(\\)2492 2849 y Fs([)2323 3028 y Fj(K)2379 3036 y Fg(i)2405 3028 y Fp(6)p Fq(=)p Fj(O)2506 3036 y Fg(i)2533 3028 y Fj(;K)2609 3036 y Fg(i)2634 3028 y Fp(6)p Fq(=)p Fj(P)2727 3036 y Fg(i)2768 2928 y Fx(Lvars)7 b FE(\()p Fw(K)3079 2940 y Fj(i)3107 2928 y FE(\))1208 3158 y Fv(\022)83 b Fx(Lvars)1564 3121 y Fp(")1602 3158 y FE(\()p Fw(N)1701 3170 y Fj(i)1729 3158 y FE(\))19 b Fv(\\)g Fx(Lvars)2062 3121 y Fp(#)2100 3158 y FE(\()p Fw(N)2199 3170 y Fj(i)2227 3158 y FE(\))p Fw(;)0 3335 y FE(whic)n(h)28 b(size)f(is)g Fv(\024)c Fw(w)r FE(.)38 b(Finally)-7 b(,)27 b(since)h Fu(cluster)p FE(\()p Fw(d)p FE(\))c(=)f Fu(cutset)o FE(\()p Fw(d)p FE(\))d Fv([)e Fu(context)p FE(\()p Fw(d)p FE(\),)28 b(w)n(e)g(ha)n(v)n(e)e Fv(j)d Fu(cluster)q FE(\()p Fw(d)p FE(\))h Fv(j\024)f FE(2)p Fw(w)r FE(.)125 3435 y(Therefore,)j(the)j (size)e(of)h(ev)n(ery)e(cutset)j(is)e Fv(\024)c Fw(w)r FE(,)29 b(the)f(size)g(of)g(ev)n(ery)e(con)n(text)i(is)f Fv(\024)d FE(2)p Fw(w)30 b FE(and)d(the)i(size)e(of)h(ev)n(ery)e (cluster)0 3534 y(is)h Fv(\024)c FE(3)p Fw(w)r FE(.)37 b(This)28 b(means)f(that)h(cutset)g(width,)g(con)n(text)f(width,)i(and) e(width)h(are)f Fv(\024)22 b Fw(w)r(;)14 b FE(2)p Fw(w)r(;)g FE(3)p Fw(w)22 b Fv(\000)c FE(1,)27 b(resp)r(ectiv)n(ely)-7 b(.)p 3642 3509 48 4 v 3642 3559 4 50 v 3686 3559 V 3642 3562 48 4 v 0 3808 a Fy(References)42 3990 y FE([1])41 b(Hans.)24 b(L.)g(Bo)r(dlaender.)30 b(A)24 b(linear)g(time)g(algorithm) f(for)h(\014nding)g(tree-decomp)r(ositions)f(of)h(small)g(treewidth.)31 b Fx(SIAM)171 4089 y(Journal)e(of)i(Computing)p FE(,)d (25\(6\):1305{1317,)23 b(1996.)42 4253 y([2])41 b(Craig)26 b(Boutilier,)h(Nir)h(F)-7 b(riedman,)27 b(Mois)n(\023)-39 b(es)26 b(Goldszmidt,)i(and)f(Daphne)h(Koller.)36 b(Con)n(text{sp)r (eci\014c)26 b(indep)r(endence)171 4353 y(in)33 b(ba)n(y)n(esian)f(net) n(w)n(orks.)52 b(In)33 b Fx(Pr)l(o)l(c)l(e)l(e)l(dings)j(of)g(the)f (12th)g(Confer)l(enc)l(e)h(on)f(Unc)l(ertainty)g(in)g(A)n(rti\014cial)g (Intel)t(ligenc)l(e)171 4453 y(\(UAI\))p FE(,)27 b(pages)f(115{123,)e (1996.)42 4616 y([3])41 b(Gregory)24 b(F.)i(Co)r(op)r(er.)33 b(Ba)n(y)n(esian)24 b(b)r(elief-net)n(w)n(ork)h(inference)h(using)f (recursiv)n(e)f(decomp)r(osition.)34 b(T)-7 b(ec)n(hnical)25 b(Rep)r(ort)171 4716 y(KSL-90-05,)f(Kno)n(wledge)i(Systems)i(Lab)r (oratory)-7 b(,)25 b(Stanford,)i(CA)h(94305,)e(1990.)42 4880 y([4])41 b(Adnan)27 b(Darwic)n(he.)36 b(Decomp)r(osable)27 b(negation)g(normal)g(form.)36 b Fx(Journal)30 b(of)g(the)g(A)n(CM)p FE(.)37 b(T)-7 b(o)28 b(app)r(ear.)42 5044 y([5])41 b(Adnan)28 b(Darwic)n(he.)39 b(Conditioning)28 b(algorithms)f(for)g(exact)h(and)g (appro)n(ximate)f(inference)h(in)h(causal)e(net)n(w)n(orks.)38 b(In)171 5144 y Fx(Pr)l(o)l(c)l(e)l(e)l(dings)28 b(of)h(the)g(11th)f (Confer)l(enc)l(e)h(on)g(Unc)l(ertainty)e(in)h(A)n(rti\014cial)h(Intel) t(ligenc)l(e)g(\(UAI\))p FE(,)c(pages)g(99{107,)e(1995.)42 5308 y([6])41 b(Adnan)34 b(Darwic)n(he.)56 b(Compiling)34 b(kno)n(wledge)f(in)n(to)h(decomp)r(osable)g(negation)f(normal)g(form.) 57 b(In)34 b Fx(Pr)l(o)l(c)l(e)l(e)l(dings)j(of)171 5407 y(International)30 b(Joint)f(Confer)l(enc)l(e)i(on)f(A)n(rti\014cial)g (Intel)t(ligenc)l(e)g(\(IJCAI\))p FE(,)e(pages)e(284{289,)f(1999.)1908 5656 y(29)p eop %%Page: 30 30 30 29 bop 42 90 a FE([7])41 b(Adnan)c(Darwic)n(he.)63 b(Dtrees:)56 b(A)37 b(new)g(graphical)e(mo)r(del)i(for)f (structure{based)g(reasoning.)62 b(T)-7 b(ec)n(hnical)36 b(Rep)r(ort)171 190 y(D{107,)26 b(Computer)h(Science)h(Departmen)n(t,)f (UCLA,)i(Los)d(Angeles,)i(Ca)f(90095,)e(1999.)42 351 y([8])41 b(Adnan)21 b(Darwic)n(he.)26 b(Utilizing)c(device)g(b)r(eha)n (vior)e(in)i(structure{based)e(diagnosis.)25 b(In)d Fx(Pr)l(o)l(c)l(e)l (e)l(dings)j(of)g(International)171 451 y(Joint)k(Confer)l(enc)l(e)i (on)f(A)n(rti\014cial)g(Intel)t(ligenc)l(e)g(\(IJCAI\))p FE(,)e(pages)e(1096{1101,)e(1999.)42 612 y([9])41 b(R.)28 b(Dec)n(h)n(ter.)36 b(Constrain)n(t)26 b(net)n(w)n(orks.)35 b Fx(Encyclop)l(e)l(dia)e(of)e(A)n(rti\014cial)f(Intel)t(ligenc)l(e)p FE(,)e(pages)f(276{285,)d(1992.)0 773 y([10])41 b(R.)27 b(Dec)n(h)n(ter)f(and)g(J.)h(P)n(earl.)34 b(T)-7 b(ree)26 b(clustering)g(for)g(constrain)n(t)g(net)n(w)n(orks.)33 b Fx(A)n(rti\014cial)d(Intel)t(ligenc)l(e)p FE(,)e(pages)d(353{366,)171 873 y(1989.)0 1034 y([11])41 b(Rina)29 b(Dec)n(h)n(ter.)40 b(Buc)n(k)n(et)29 b(elimination:)40 b(A)29 b(unifying)h(framew)n(ork)d (for)h(probabilistic)h(inference.)41 b(In)29 b Fx(Pr)l(o)l(c)l(e)l(e)l (dings)j(of)171 1134 y(the)e(12th)g(Confer)l(enc)l(e)h(on)f(Unc)l (ertainty)f(in)h(A)n(rti\014cial)g(Intel)t(ligenc)l(e)h(\(UAI\))p FE(,)c(pages)f(211{219,)e(1996.)0 1295 y([12])41 b(Rina)32 b(Dec)n(h)n(ter.)50 b(T)-7 b(op)r(ological)30 b(parameters)h(for)g (time-space)h(tradeo\013.)50 b(In)32 b Fx(Pr)l(o)l(c)l(e)l(e)l(dings)j (of)g(the)f(12th)h(Confer)l(enc)l(e)171 1395 y(on)29 b(Unc)l(ertainty)h(in)g(A)n(rti\014cial)g(Intel)t(ligenc)l(e)g(\(UAI\)) p FE(,)d(pages)g(211{219,)d(1996.)0 1556 y([13])41 b(F.)28 b(J.)f(D)423 1536 y(\023)432 1556 y(iez.)37 b(Lo)r(cal)27 b(conditioning)g(in)h(ba)n(y)n(esian)e(net)n(w)n(orks.)35 b Fx(A)n(rti\014cial)30 b(Intel)t(ligenc)l(e)p FE(,)f(87\(1\):1{20,)c (1996.)0 1717 y([14])41 b(H.)f(N.)f(Djidjev)i(and)e(J.)h(R.)f(Gilb)r (ert.)73 b(Separators)37 b(in)j(graphs)e(with)i(negativ)n(e)e(and)h(m)n (ultiple)i(v)n(ertex)d(w)n(eigh)n(ts.)171 1817 y Fx(A)n(lgorithmic)l(a) p FE(,)29 b(23:57{71,)24 b(1999.)0 1978 y([15])41 b(Alan)26 b(George.)33 b(Nested)26 b(dissection)f(of)h(a)g(regular)e(\014nite)j (elemen)n(t)f(mesh.)34 b Fx(SIAM)28 b(Journal)h(of)g(Numeric)l(al)f(A)n (nalysis)p FE(,)171 2078 y(10\(2\):345{363,)23 b(1973.)0 2239 y([16])41 b(E.J.)23 b(Horvitz,)i(H.J.)g(Suermondt,)g(and)f(G.F.)h (Co)r(op)r(er.)31 b(Bounded)24 b(conditioning:)35 b(Flexible)25 b(inference)f(for)g(decisions)171 2338 y(under)f(scarce)g(resources.)29 b(In)24 b Fx(Pr)l(o)l(c)l(e)l(e)l(dings)j(of)g(Confer)l(enc)l(e)h(on)e (Unc)l(ertainty)g(in)g(A)n(rti\014cial)h(Intel)t(ligenc)l(e,)i (Windsor,)171 2438 y(ON)p FE(,)e(pages)g(182{193.)e(Asso)r(ciation)i (for)h(Uncertain)n(t)n(y)f(in)h(Arti\014cial)g(In)n(telligence,)g(Moun) n(tain)g(View,)g(CA,)h(August)171 2538 y(1989.)0 2699 y([17])41 b(Cecil)36 b(Huang)f(and)h(Adnan)g(Darwic)n(he.)61 b(Inference)36 b(in)g(b)r(elief)g(net)n(w)n(orks:)52 b(A)37 b(pro)r(cedural)d(guide.)62 b Fx(International)171 2799 y(Journal)29 b(of)i(Appr)l(oximate)f(R)l(e)l(asoning)p FE(,)e(15\(3\):225{263,)c(1996.)0 2960 y([18])41 b(F.)34 b(V.)h(Jensen,)h(S.L.)f(Lauritzen,)g(and)g(K.G.)f(Olesen.)57 b(Ba)n(y)n(esian)32 b(up)r(dating)j(in)f(recursiv)n(e)f(graphical)g(mo) r(dels)h(b)n(y)171 3059 y(lo)r(cal)27 b(computation.)36 b Fx(Computational)31 b(Statistics)f(Quarterly)p FE(,)e(4:269{282,)c (1990.)0 3221 y([19])41 b(S.)29 b(L.)f(Lauritzen)g(and)h(D.)g(J.)g (Spiegelhalter.)39 b(Lo)r(cal)28 b(computations)g(with)h(probabilities) f(on)h(graphical)e(structures)171 3320 y(and)k(their)g(application)g (to)g(exp)r(ert)g(systems.)47 b Fx(Journal)33 b(of)h(R)l(oyal)g (Statistics)f(So)l(ciety,)i(Series)e(B)p FE(,)f(50\(2\):157{224,)171 3420 y(1988.)0 3581 y([20])41 b(Z.)34 b(Li)g(and)g(B.D.)g(D'Am)n (brosio.)55 b(E\016cien)n(t)34 b(Inference)g(in)g(Ba)n(y)n(es)f(Net)n (w)n(orks)f(as)h(a)h(Com)n(binatorial)e(Optimization)171 3681 y(Problem.)j Fx(International)30 b(Journal)g(of)h(Appr)l(oximate)f (R)l(e)l(asoning)p FE(,)e(11:55{81,)c(1994.)0 3842 y([21])41 b(Ric)n(hard)24 b(Lipton,)j(Donald)e(Rose,)h(and)f(Rob)r(ert)h(Andre)f (T)-7 b(arjan.)33 b(Generalized)25 b(nested)h(dissection.)33 b Fx(SIAM)28 b(Journal)171 3942 y(of)i(Numeric)l(al)g(A)n(nalysis)p FE(,)f(16\(2\):346{358,)23 b(1979.)0 4103 y([22])41 b(Ric)n(hard)30 b(Lipton)i(and)g(Rob)r(ert)f(Andre)h(T)-7 b(arjan.)48 b(A)32 b(separator)d(theorem)i(for)g(planar)g(graphs.)47 b Fx(SIAM)34 b(Journal)f(of)171 4202 y(Applie)l(d)e(Mathematics)p FE(,)e(36\(2\):177{189,)24 b(1979.)0 4364 y([23])41 b(D.)28 b(Maier.)36 b Fx(The)31 b(The)l(ory)g(of)f(R)l(elational)h(Datab)l (ases)p FE(.)37 b(Computer)28 b(Science)f(Press,)f(Ro)r(c)n(kville,)h (Maryland,)g(1983.)0 4525 y([24])41 b(G.)26 b(L.)g(Miller)g(and)g(J.)g (H.)g(Reif.)35 b(P)n(arallel)24 b(tree)i(con)n(traction)e(and)i(its)g (application.)34 b(In)26 b Fx(Pr)l(o)l(c.)j(26th)h(IEEE)f(Symp.)g(on) 171 4625 y(F)-6 b(oundations)30 b(of)g(Computer)h(Scienc)l(e)p FE(,)d(pages)e(478{489,)e(P)n(ortland,)j(OR,)g(1985.)0 4786 y([25])41 b(Judea)29 b(P)n(earl.)44 b Fx(Pr)l(ob)l(abilistic)34 b(R)l(e)l(asoning)f(in)f(Intel)t(ligent)h(Systems:)43 b(Networks)33 b(of)g(Plausible)g(Infer)l(enc)l(e)p FE(.)46 b(Morgan)171 4885 y(Kaufmann)27 b(Publishers,)f(Inc.,)i(San)g(Mateo,)f (California,)f(1988.)0 5047 y([26])41 b(Mark)d(A.)i(P)n(eot)f(and)g (Ross)g(D.)h(Shac)n(h)n(ter.)71 b(F)-7 b(usion)40 b(and)f(propagation)e (with)k(m)n(ultiple)f(observ)-5 b(ations)37 b(in)j(b)r(elief)171 5146 y(net)n(w)n(orks.)35 b Fx(A)n(rti\014cial)30 b(Intel)t(ligenc)l(e) p FE(,)f(48\(3\):299{318,)23 b(1991.)0 5308 y([27])41 b(Arnie)19 b(Rosen)n(thal.)24 b(Computing)c(the)g(reliabilit)n(y)f(of)h (complex)f(net)n(w)n(orks.)k Fx(SIAM)f(Journal)h(of)g(Applie)l(d)h (Mathematics)p FE(,)171 5407 y(32\(2\):384{393,)f(1977.)1908 5656 y(30)p eop %%Page: 31 31 31 30 bop 0 90 a FE([28])41 b(R.)28 b(Shac)n(h)n(ter,)e(S.K.)i (Andersen,)g(and)f(P)-7 b(.)28 b(Szolo)n(vits.)36 b(Global)27 b(Conditioning)g(for)g(Probabilistic)f(Inference)i(in)g(Belief)171 190 y(Net)n(w)n(orks.)35 b(In)28 b Fx(Pr)l(o)l(c.)i(T)-6 b(enth)30 b(Confer)l(enc)l(e)h(on)e(Unc)l(ertainty)h(in)g(AI)p FE(,)d(pages)f(514{522,)f(Seattle)i(W)-9 b(A,)29 b(1994.)0 356 y([29])41 b(R.)26 b(Shac)n(h)n(ter,)g(B.D.)g(D'Am)n(brosio,)g(and)g (B.)g(del)g(F)-7 b(a)n(v)n(ero.)33 b(Sym)n(b)r(olic)26 b(Probabilistic)f(Inference)h(in)g(Belief)h(Net)n(w)n(orks.)171 456 y(In)g Fx(Pr)l(o)l(c.)k(Conf.)g(on)f(Unc)l(ertainty)f(in)h(AI)p FE(,)e(pages)e(126{131,)e(1990.)0 622 y([30])41 b(Prak)-5 b(ash)26 b(P)-7 b(.)28 b(Sheno)n(y)-7 b(.)38 b(A)29 b(v)-5 b(aluation{based)27 b(language)f(for)i(exp)r(ert)g(systems.)38 b Fx(International)31 b(Journal)f(of)i(Appr)l(oxi-)171 721 y(mate)d(R)l(e)l(asoning)p FE(,)f(5\(3\):383{411,)c(1989.)0 887 y([31])41 b(Rob)r(ert)27 b(E.)g(T)-7 b(arjan.)36 b(Decomp)r(osition)28 b(b)n(y)f(clique)g(separators.)35 b Fx(Discr)l(ete)29 b(Mathematics)p FE(,)h(55:221{232,)23 b(1985.)0 1053 y([32])41 b(Nevin)26 b(Lian)n(w)n(en)f(Zhang)h(and)g(Da) n(vid)g(P)n(o)r(ole.)33 b(Exploiting)25 b(causal)g(indep)r(endence)i (in)g(ba)n(y)n(esian)d(net)n(w)n(ork)h(inference.)171 1153 y Fx(Journal)k(of)i(A)n(rti\014cial)f(Intel)t(ligenc)l(e)h(R)l (ese)l(ar)l(ch)p FE(,)d(5:301{328,)c(1996.)1908 5656 y(31)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF