CTW0¥ Workshop on Graphs and Combinatorial Optimi8ation
Transcription
CTW0¥ Workshop on Graphs and Combinatorial Optimi8ation
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V.XKyTty ¬ * k © ¬ j g U UTx ^ z^ V^ h abWced #gf d ; ji ; k ml j j k ml qortsuOvxwrtsuOv /y u vz!{|sW}<i=~w k ml' z k qprtsuOvxw EG4SUV< H 02<M5&1w5&4 NE 9 EG4UVK 9 5@s i C 5&45 = NE 9 EG4UVK 9 514U I,C ;LUV45 O0R;OM C 5FNEG x C E"sx5&Pw5&4802<NEG445N&M 6ADC 0R; UV45 N&024N&3 9 UV<M:14U I,C ; 4 s:5 929= @<E"sL< 02<N 9 3;0REG<EVt I,9 UV<vUV4 tEG4 I,9 5&{5&<MD14U I,C I U I & 5 4 f 6ADC 5S;3,KZ02P@0RZ,5Z x = NE 9 EG402<,1 7 E 9 EG4 = tUV0 92H UF;3,K;5&M!EVt EVt02<N 9 3;0REG<YNEG<MUV02<;OM C 5 I 4E"Pw5{;EG{5 e ? = NEG I,9 5&M5 I 4EGK 9 5&{; x = NE 9 EG402<,1 6 ' 7 024N&3 9 UV<M14U I,C ; ,M02{5QNEG I,9 5 02M H LWTJ^ N^?}L p; h r w r w ; *«5y3Qy v!x # E n r w uOiueee=u Gq ^i y3{¤y3{¤y >i v ( { q r w r[qw r w r[qw rt$w rtxw c2 q - / c2 /q *I5y3Qy v!x # yTS% h ' q gq *«5y3Qy v!x # > y s{ /q q *«5yTy U s q s Yl ; (q Q¡ |7 & dp \R 9 C7 9 q i U3xHx~sU (( v # xM{¤suxMt > y s{ (7p 9 *I5y3Qy v!x #3( q r[qw/ ¡q ¢ 5y3Qy *£SeU3{)v! vs ( ¤ o b P Y¨ ¦¥ «2 ^§ 4 4 2 E§|4 4 2 ¨©«ªo¬'C®¯±°²e³e³e´^µ·¶¹¸Eº%» ¼µ·½·½|¾¼µ¿¸g°¶gµÀ5¨ÁÂeÃÅÄÇÆ?¾½ÉÈ^ÃËÊEÌeºÆ;È,ÆΰÐÏ=¶$´ÒѹÓ<¶$³%Ϲ¬P¬' EG4|U102Pw5&<14U I,C c ME 14U I,C ; UV<Z sL02M C j 0 6 5 6 U{TU I,I 02<,1 ;3N C EVt J6 }~5;U H M C UVM = NE 9 EG4UVK 9 5 6 0R; NE 9 EG402<,1w;"UV<Z02M EVtOZ,5N&0RZ02<,1s ADC 3;" = NE 9 EG402<,1 K55&< UV< 02 = NE 9 EG402<,1 _ <vUVM3,4U 9 0R;YU 0R; I,9 5&M5{14U I,C TU H = NE 9 EG4UVK 9 5 j6 0R;;3 I,I EG4M5Z K H N 9 UG;;5;YUV45 ADC 5EG45&{; ADC 5 ;M 7 UV<Z Os 5&<M3,4 H7 tu4EG 02<,0R;M4 H EVt 8Z3N"UVM0REG<* N 0R5&<N5 BI EG4M; UV<Z & 9 UVK 6 B3,0R; 6 H EGME = 3 6 UGN 6 I 35 02TU X 02ME C 024E @3,0R; 6 H EGME = 3 6 UGN 6 I 7 UG; U sL0 929 J6 0R;Z,5&<EGM5ZK H = NE 9 EG402<,1 I 4EGK 9 5& TUV<Z K5; C EsL< ?84EG14UV 3 9 M3,45 EVt ,5Z C 5&M C 5&4 14U I,C I 4EGK 9 5&{; $6 Z,5N&0R;0REG< N"U 929 5Z C 0RN C EG4FUV< H EVt:Z,5N&0RZ02<,1s wUV<Z U I UV< 6 UV<Z M C 5 45 9 UVM5Z ME U M C 5&024Y;M43N&M3,45 9 UVM5&4 6 N&0R5&<M0 vN EG{5 UV<Z $6ADC 5L02<M5&4NEG<,<5N&M0REG<;xK5&M$sx55&< , @ NEG<;0RZ,5&45Z 0t EVtM C 5M4UGZ02M0REG<vU 9 k K5 3N C EVtxEG4Z,5&4 I 4EGK 9 5& 1w5&<5&4U 9 0 UVM0REG< EVt14UVTUV4tEG4{;s:5&45D02<BPw5;M021UVM5Z02< I 4EGK 9 5& I EG4MUV<BMYM C 5&{5D5 6 1 6 ADC 0R;45;5"UV4N C I 4EGK 9 5& nNEG J6 = NE 9 EG4UVK 9 50R;M C 5 0R; W 02Pw5&< = NE 9 EG402<,1EVtOUJ102Pw5&<`02< I 3,M14U I,C I 4EGK 9 5&{;45 9 UVM5Z`ME LUV<Z B3,02PGU 9 5&<BM 29 H c C 5&M C 5&4 C UG;8K55&<T;M3Z0R5Z{02<{PGUV40REG3;ONEG<M5 M; C EG{EG{EG4 I,C 0R;{;xUV<Z|M C 5DM C 5EG4 H 02<N 9 3Z,5 0R;U 9 ;E{N"U 929 5ZpUV< EVt LME SUV45UGZ UGN5&<MPw5&4M0RN5;EVt C 5&M C 5&4M C 5&45Q0R;FUV< = NE 9 EG402<,15 @0R;M; 6 0tDUV< I 4EGK 9 5& FUV<Z C EG{EG{EG4 I,C 0R; U 0R; UTU I,I 02<,1 {EVt I 45;5&4P@02<,1TTU I,I 02<,1EVt 0R;UV<5Z1w5 M C UVM 0R;SZ,5N&0RZ02<,1Ys 0R; 6FADC 5&<*M C 5 W ME F;3N C 3N C |k !U Pw5&4M0RN5;EG<M C 5;UV{55Z1w5Y45N5&02Pw5M C 5;UV{5NE 9 EG4 6 EVt ME e UV<Z5Z1w5{;5&M M C UVMJ<EM$s:E k UV45 UGZ UGN5&<M Pw5&4M0RN5;EVt 14U I,C Pw5&4M5 ~;5&M U = 6ADC 5FNEG<Pw5&4;5;MUVM5&{5&<BM; C 0R5&4UV4N CBH EG45E"Pw5&4"s:5 ;?on = NE 9 EG4UVK 9 514U I,C ;SUV45 EVtUQN H N 9 5EVtmEG4Z,5&4 = NE 9 EG4UVK 9 5{14U I,C ; 6 x k m; l j ?pn i = NE 9 EG4UVK 9 5QUV<Z I 45;5&<BM;M C UVMM C 5DUVKE"Pw5D02<N 9 3;0REG<JN"UV<K5x;3,KZ02P@0RZ,5ZK H = NE 9 EG402<,1w;v02<N 9 3Z02<,1{M C 5 V)sX` y . ( 0 q k N 9 UG;; C UG; M5&4{;TUV45 4UV<M = 02< = F0RZ PTP A UVK 9 5 <N 9 3;0REG< %&$ (,- /,%- "$"$" qortsuOvxw EG< Ðl Åk LUV<Z45 9 UVM0REG<`sL02M C W , VUV<Z '$ *)- .0/&-1 02&%- 3)4)%- 3$$)%- "$"!" ! ()$ 2&- 3)%- "$"!" k #"$"!" *)$ +"$"" 3)4)-.3$$)-5"$"!" 3))%- 3)%)%- 3')%-5"!"$" ""$" q q76 i y3{¤y3{¤y Mi v$ U3WÉX^s98 v 0 U3sxMt q /q 6 " 5 y s q h 7R 9 q q 6 n z A eu5A <ueee'u5A<;Òz {|sW}<i=~ 6q Ò7q 6t q:6 5y sy S q h s uv ·U3xMt #3 U Mi rt>s =MA u5A <ueeeu5A<;Pw @? u n ueeeuTs 1 n c2 1 Br ADC<EsWw 1 rBADCFEsWw A u5A <ueeeu5A<; o q t r s O u x v w t r >=Ov uOv ?n ueee=u{|sW}<i=~w s n z vz {|sW}<i=~ P P ; P HGJI >I kl q q KMLONQPSRTN<UWV ( s5sCÅU Y XzjKj y U3xxX£v!xMts # s +( ; ji suv n w [ r[qprts ?¢n uOvxwTw Z r[qortsuOvxwT# ; n w G r[qor ; v uOvxwT\w G r[qor ; v ? n uOvxwTw U3x^] l v ( t i s y s)yTS qpr ; v uOvxw (U3xS] Z r[qor v 1 uOvxwT5 ; ? n n w G r[qorTrmi ; ? n w v uOiPvxwTw+G r[qprTrmi ;¤? n w v ?¢n uOiPvxwTw UTxS] k ml' v ( t i s y s Z r[qorTrmi ;¤? n w v 1 uOiPvxwT# yTS qprTrmi w v uOiPvx_w X ` PaR PSb!bcRTdeVSf!V y U3xxX vWxMts # s ( ; i r[qor ; u wTg w G r[qpr ; ?Ln u wTwhG r[qpr ;F? ; iu wTwgG F ; j ? i 8 ; L ? n r[qp; r ? u wTg w G r[qor r wÇu wT_w X h y s5y 0 s Ðl U3Sx ] k ml' U s t i s y s ( yTS qor u w UTxS] qor iu w s ( s/"twv 0 sÉX X Z X y U3xxoX n zs)z n ¿UTxÅU qprtsu w *I5y3Qy v!x # KMLONQPSRTN<Ulk Z ·U3xÅU (qo$r mu w *«y3y vWx # > y s{ v ( n vWx 5 x p r w ty ( yT 0 s X¤Z ·U3xÅU Yk ml' *«y3y vWx # > y Qsu{ v ( Z * > y s{ v ( Z *«y3{ Qs"ts X ; ¥Yt i s `v ( s vwtv ( vWq 5y3{ suts6S"y U3xxX£v!xMts # s ji X I,9 UV02<,02<,1M C 5J;MUVM5&{5&<M;sx5J; C E"sQ*UG; tE 929 E"sS; 6 Z,5 <5ZptEG4 5 $k a 0R;U 3 I NEG<MUV02<;DU3,<,0 35 sx5N"U 929 ME a v UGZ UGN5&<M0t8UV<ZEG< 92H 8;3,K,14U I,C 6 0t f xEG4 c UV<Z v I,9 5&M5 M C UVM5&Pw5&4 H 02< j UV<Z UV45 d14U I,C I,9 5U 929 NEG 14U I,C C EG{EG{EG4 I,C 0R; 0R;OUNEG45FUV<ZTUGZ02M;:U I E;02M02Pw5|02<BM5&1w5&4; c EG4 UV<Z 14U I,C*6 vEG45 ,UV I 4EPw5&< MLsxUG; C 0RN C s C UG;SM C 5 Pw5&4M5 ;5&M B M C UVMM$sxE14U I,C ; I 4E I 5&4S;3,K,14U I,C*6 ME{U I,9 5&{5&<M; EVtE@Z,ZN H N 9 5;SUV45QNEG45; 6 ME0R;EG{EG4 I,C 0R; *M C 5 k }~5|;U H = NE 9 EG4UVK 9 5UV45 5 3,02PU 9 5&<MtuEG4UV< H C EG{EG{EG4 I,C 0R; 0t02MZ,E@5;L<EGMUGZ02MFU 14U I,C ;"E@Z,ZN H N 9 5;"UV<ZNEG EVt = NE 9 EG4UVK 9 5UV<Z 0t wM C 5 @ M$s:ETPw5&4M0RN5; UV<Z UV45 j6 B }~5xTUV02< 92HQI 4E"Pw5DMs:EM C 5EG45&{;!tEG4M C 5x;3,KN 9 UG;;EVtN&024N&3 9 UV<M14U I,C ; {UG;StE 929 E"sS; 67 tEG4 I 4E I 5&4;3,K;5&MSEVt 0R;U EG4E 929 UV4 H 6 |0R;FEGK,MUV02<5Ztu4EG J0R;UN H N 9 5EVtEG4Z,5&4 [ 0R;SM C 5QNEG UV<Z b\| ^ i ADC 5EG45& 6 Z,5&<EGM5; M C UVM I,9 5&{5&<MF14U I,C EVtU14U I,C 6 ^ i ^ ^ W ^ k ^ W k x q ^ k b^ k k 7 $k x k i E 9 EG4 = tUV0 9 0R5; ADC 5EG45& ^ i P 4 C UPw5{M C 5TU 9 45"UGZ H= @<E"sL<KvUG;0RN02<N 9 3;0REG<; UG;tuE 929 EsS; C 0R5&4UV4N CH 0R;FUJ;3,KZ02P@0RZ,5Z A ;55 PTP UVK 6 6ADC 5{02<N 9 3;0REG<~02< EVtM C 5;502<N 9 3;0REG<; 6 y U3x X v!xMts # s +( ; n uw ji r l w#G r 'l _w Xrh y s/y 0 s $ r wG r k 9T wG r 'w r k 'w U3x^]Ð r k 9T Çw\G r k 9yx Çw_X KMLONQPSRTN<U{z|t~} v y U3xxX¤vWxMts # s ; ji Ë r YlEw#G r k ml OwG r Ð'l Ç_w X KMLONQPSRTN<Usrut ©BvO uWTX xX i x F h EG4 1w5&<5&4U 9 14U I,C ;"M C 5|NEG I,9 5 02M H e F? = NEG I,9 UV<vUV414U I,C ; UV<Z02M0R;;M0 929 ;02M3vUVM0REG<0R; sx5 929= 3,<Z,5&4;ME@EBZ q uW ^ uW EVt uW x = NE 9 EG402<,1 £7 :9 e I,9 5&M5 E I 5&< 6 tEG4 NEG ^ uW ^ i 0R;xK,0 I UV4M02M5EGM C 5&4sL0R;5 02MD0R; tEG4 Ji x $6 I 4EGK 9 5& Es:5&Pw5&4",M C 5 F55Z 9 5;;ME;bU H M C 5 S%h I,9 5&M514U I,C ; @.. 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