!"#$%$&'&()&*+,"%-.&*%'+/#01'(+234-5)+6789: - PDF document

Cmput 651 - Clique Trees {20,24}/10/2008 !"#$%$&'&()&*+,"%-.&*%'+/#01'(+234-5)+6789: 3'&;51+<"11( /%)).1=+>"#=? @ABCADEF8BFABBG H1%0&?I:+J#''1"KL"&104%?+3.M+N 8 O-%*1+#P+)#-&*( O14%?)&*( T?P1"1?*1 S1%"?&?I Q&(*"1)1 Q&"1*)10 R?Q&"1*)10 3#?)&?5#5( A

Cmput 651 - Clique Trees {20,24}/10/2008 [5)'&?1 !"#$%&'()&&*'+,-'./0)-+"'1)+2/* \%"&%$'1+1'&4&?%)&#?+K]+*'&;51+)"11 3'&;51+)"11+K]+Y%"&%$'1+1'&4&?%)&#?^ 3%'&$"%)&#? >1'&1P+5-0%)1+41((%I1+-%((&?I ,1?1"%'+;51"&1( >5&'0&?I+*'&;51+)"11( _ 3'&;51+)"11( 3'&;51( Z @ZC>C3E a @>C3CQE V > 3 @3CQCUE W Q U @QCUCLE ` L U%*.+10I1+"1-"1(1?)(+%+(1-(1)M+<.1+(1-(1)+O VCW +$1)=11?+)=#+ *'&;51(+3 V +%?0+3 W +&(+).1+&?)1"(1*)&#?+#P+3 V +%?0+3 W +2@3CQE+&?+).1+ 1X%4-'1+%$#Y19M D

Cmput 651 - Clique Trees {20,24}/10/2008 3'&;51+)"11(+ 2Z'(#+(11+JL+Q1P&?&)&#?+DM7M87M9 8 () +Q1P&?&)&#?:+Z+)"11+<+&(+%+ ."#$%&'()&& +P#"+%+I"%-.+b+&P &9+1%*.+?#01+&?+<+*#""1(-#?0(+)#+%+*'&;51+&?+b &&9+1%*.+4%X&4%'+*'&;51+&?+b+*#""1(-#?0(+)#+%+?#01+&?+< &&&9+1%*.+(1-(1)+O &Cc +*5)(+b+&?)#+)=#+-&1*1(+ + 2Y%"&%$'1(+#?+0&PP1"1?)+(&01(+#P+*5)+%"1+?#)+*#??1*)10+ $d+%+-%).9 7 UX%4-'1+#P+*5)+$d+(1-(1) 3'&;51( Z @ZC>C3E a @>C3CQE V > 3 @3CQCUE W Q U @QCUCLE ` L (1-(1)+O VCW +$1)=11?+*'&;51(+3 V +%?0+3 W +*5)(+).1+I"%-. 6

Cmput 651 - Clique Trees {20,24}/10/2008 3.#"0%'+I"%-.(+%?0+*'&;51+)"11( + 8/&0)&5 :+UY1"d+5?0&"1*)10+*.#"0%'+I"%-.+.%(+%+ *'&;51+)"11M+ 2O11+JL+<.1#"14+DM7M869 Z a V > 3 W Q U ` L e [5)'&?1 3'&;51+)"11(+%?0+*.#"0%'+I"%-.( 3+)#+4"&'&"#5#,+(#0,'67'."#$%&'()&& 3'&;51+)"11+K]+Y%"&%$'1+1'&4&?%)&#? 3%'&$"%)&#? >1'&1P+5-0%)1+41((%I1+-%((&?I ,1?1"%'+;51"&1( >5&'0&?I+*'&;51+)"11( G

Cmput 651 - Clique Trees {20,24}/10/2008 \%"&%$'1+1'&4&?%)&#?+1X%4-'1+ 2O11+JL+UX%4-'1+GM_M_9 O544%"d+#P+Y%"&%$'1+1'&4&?%)&#?+()1-(+)#+4%"I&?%'&h1+#5)+i: N 3'5()1"+I"%-.+P#"+Y%"&%$'1+1'&4&?%)&#?+ 2O11+JL+NM8M89 • +U%*.+?#01+&?+*'5()1"+I"%-.+ "1-"1(1?)(+%+P%*)#"+ � V f(+(*#-1M+ • +U%*.+10I1+"1-"1(1?)(+%+41((%I1+ P%*)#"+g & f(+(*#-1M 3'5()1"+,"%-. 8B

Cmput 651 - Clique Trees {20,24}/10/2008 3'5()1"+I"%-.+P#"+Y%"&%$'1+1'&4&?%)&#?+ 2O11+JL+NM8M89 3'5()1"+,"%-. T?+Y%"&%$'1+1'&4&?%)&#?C+1%*.+?#01+I1?1"%)1(+%+?1=+P%*)#"+g+2*%''10+ %+41((%I19+=.&*.+&(+-%((10+)#+).1+?1X)+?#01M+<.1+?1X)+?#01+)%j1(+ &?+%''+g+41((%I1(C+45')&-'&1(+).14+=&).+&)(+#=?+ � P%*)#"C+1'&4&?%)1(+ k8+Y%"&%$'1+)#+-"#05*1+%+?1=+g+41((%I1C+%?0+-%((1(+g+#?M 88 3'5()1"+I"%-.+ 2O11+JL+Q1P&?&)&#?+NM8M89 Q1P&?&)&#?:+,&Y1?+(1)+L+#P+P%*)#"(+#Y1"+ ! C + %+ ."%*(&)'1)+2/' J+&(+%?+5?0&"1*)10+I"%-.+(5*.+).%): + K+?#01+&+"1-"1(1?)(+%+*'5()1"+2(1)9 C i � � + K+P%4&'dK-"1(1"Y&?I:+P#"+1%*.+P%*)#"+ � +&?+LC scope ( � ) � C i + + 1X&()(+k+8+?#012(9+&+=&). C i � C j + K+10I1+3 & K3 c +"1-"1(1?)(+(1-(1)+ 8A

Cmput 651 - Clique Trees {20,24}/10/2008 H5??&?I+&?)1"(1*)&#?+-"#-1")d Q1P&?&)&#?: + ,&Y1?+*'5()1"+)"11+<+#Y1"+P%*)#"(+LC + <+.%(+).1+ )%,,#,1'#,(&)*&.(#0,'2)02&)(9 +41%?(: + TP+Y%"&%$'1+V+&(+&?+)=#+*'5()1"(+3 & +%?0+3 c C + ).1?+V+&(+&?+1Y1"d+*'5()1"+&?+25?&;519+-%).+P"#4+3 & +)#+ 3 c M 2O11+JL+Q1P&?&)&#?+NM8M_M9 8_ H5??&?I+&?)1"(1*)&#?+-"#-1")d 3'5()1"+,"%-. 3'5()1"+)"11+(%)&(P&1(+"5??&?I+&?)1"(1*)&#?+-"#-1")dM 1I:+,+&(+&?+*'5()1"(+A+%?0+DC+%(+=1''+%(+).1+&?)1"Y1?&?I+*'5()1"(+_+%?0+ 7M+ 8D

Cmput 651 - Clique Trees {20,24}/10/2008 H5??&?I+&?)1"(1*)&#?+-"#-1")d+%?0 Y%"&%$'1+1'&4&?%)&#? 8/&0)&5 : + TP+<+&(+%+*'5()1"+)"11+&?05*10+$d+Y%"&%$'1+1'&4&?%)&#?C+ ).1?+<+(%)&(P&1(+).1+"5??&?I+&?)1"(1*)&#?+-"#-1")dM + 2%?0+).1"1P#"1+<+&(+%+*'&;51+)"11C+(11+?1X)+('&019M+ 2O11+JL+<.1#"14+NM8M87+P#"+-"##PM9 87 3'&;51+)"11(+2A ?0 +01P&?&)&#?9+ 2%'(#+(11+JL+NM8MA9 A ?0 +Q1P&?&)&#?: + Z+ ."#$%&'()&& +&( + &9+%+*'5()1"+)"11 + &&9+).%)+(%)&(P&1(+"5??&?I+&?)1"(1*)&#?+-"#-1")d Q1Pf?+A+1;5&Y%'1?)+)#+1%"'&1"+01Pf?+8: Z+)"11+<+&(+%+ ."#$%&'()&& +P#"+%+I"%-.+b+&P + &9+1%*.+?#01+&?+<+*#""1(-#?0(+)#+%+*'&;51+&?+b + &&9+1%*.+4%X&4%'+*'&;51+&?+b+*#""1(-#?0(+)#+%+?#01+&?+< + &&&9+1%*.+(1-(1)+O &Cc +*5)(+b+&?)#+)=#+-&1*1( 86

Cmput 651 - Clique Trees {20,24}/10/2008 3'&;51+)"11(:+<=#+1;5&Y%'1?)+01P&?&)&#?( l#)1+1X)"%+10I1(+)#+ 4%j1+).&(+*.#"0%'M 3'&;51+)"11+(%)&(P&1(: 01Pf?+89+$%(10+#?+*.#"0%' 01Pf?+A9+$%(10+#?+Y%"&%$'1+1'&4&?%)&#? 3'&;51+<"11 8e [5)'&?1 3'&;51+)"11(+%?0+*.#"0%'+I"%-.( \%"&%$'1+1'&4&?%)&#?+K]+*'&;51+)"11 !"#$%&'()&&'67':+)#+4"&'&"#5#,+(#0, 3%'&$"%)&#? >1'&1P+5-0%)1+41((%I1+-%((&?I ,1?1"%'+;51"&1( >5&'0&?I+*'&;51+)"11( 8G

Cmput 651 - Clique Trees {20,24}/10/2008 \%"&%$'1+1'&4&?%)&#?+$%(10+#?+*'&;51+)"11( 2O11+JL+NMAM89 R(1+*'&;51+)"11(+)#+-1"P#"4+Y%"&%$'1+1'&4&?%)&#?+Y&%+ (54+-"#05*)+41((%I1+-%((&?I (5$()%?)&%'+-1"P#"4%?*1+$1?1P&)( 8N 3'&;51+)"11+41((%I1+-%((&?I 2(11+JL+NMAM8MA9 3'&;51+)"11+(54K-"#05*)+5-=%"0+-%((+%'I#"&).4: !%((+41((%I1(+5-+)#+"##)+*'&;51+3 " M L&?%'+*'&;51+-#)1?)&%'+m " n3 " ^+"1-"1(1?)(++ + + + + + + + 2&M1M+4%"I&?%'+-"#$%$&'&)d+#Y1"+"##)+*'&;519 5-()"1%4+Y(M+0#=?()"1%4 AB

Cmput 651 - Clique Trees {20,24}/10/2008 3'&;51+)"11+41((%I1+-%((&?I+ 2Z'(#+(11+JL+NMAM8M8C + NMAM8MA9 UX%4-'1+)%(j:+,&Y1?+).1+*'&;51+)"11+$1'#=+ 2$%(10+#?+?1)=#"j+%)+'1P)9C+*#4-5)1+!2i9M 3'&;51+<"11 A8 3'&;51+)"11+41((%I1+-%((&?I 2(11+JL+NMAM8M8C+NMAM8MA9 3'&;51+)"11+(54K-"#05*)+5-=%"0+-%((+(1)5-: ,&Y1?+*'&;51+)"11+<+=&).+*'&;51(+3 8 MMM3 J 8M+Q1*&01(+P#"+=.&*.+Y%"&%$'12(9+V+d#5+=%?)+)#+*#4-5)1+ ).1+4%"I&?%'+ 2P#"+?#=C+=1+%((541+%''+V+%"1+&?+#?1+*'&;51C+ $5)+(11+'%)1"+('&01(+%(+=1''+%(+JL+NM_MD 9M+ AM+O1'1*)+"##)+*'&;51+3 " +)#+$1+%+*'&;51+*#?)%&?&?I+VM _M+Z((&I?+&?&)&%'+P%*)#"(+)#+*'&;51(+(5*.+).%)+P%*)#"+ (*#-1(+%"1+*#?)%&?10+&?+).1+*'&;51(M AA

Cmput 651 - Clique Trees {20,24}/10/2008 3'&;51+)"11+41((%I1+-%((&?I+ 2Z'(#+(11+JL+NMAM8M8C+NMAM8MA9 3'&;51+<"11 )00('."#$%& &?&)&%' P%*)#"( A_ 3'&;51+)"11+41((%I1+-%((&?I 2(11+JL+NMAM8MA9 3'&;51+)"11+(54K-"#05*)+5-=%"0+-%((+2*#?)f09: 7M+!1"P#"4+(54K-"#05*)+Y%"&%$'1+1'&4&?%)&#? + ()%")+%)+'1%P+*'&;51( + -%((+41((%I1(+)#=%"0+).1+"##)M /1((%I1+*#4-5)%)&#?: 8M+P%*)#"+-"#05*)+#P+&?*#4&?I+41((%I1(+ 2P"#4+%''+ ?1&I.$#5"(+1X*1-)+3 -" 9 +%?0+3 & f(+#=?+&?&)&%'+-#)1?)&%' AM+(54+#5)+%''+Y%"&%$'1(+&?+3 & +1X*1-)+(1-(1)+2&?)1"(1*)&#?9+ $1)=11?+3 & +%?0+3 -" 23 -" o5-()"1%4+?1&I.$#5"9 AD