Optimal concave costs in the SDH context
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Optimal concave costs in the SDH context Sébastien Choplin — Jérôme Galtier — Stéphane Pérennes. N° 5201 Mai 2004. ISSN 0249-6399. ISRN INRIA/RR--5201--FR+ENG. Thème COM. apport de recherche.
(3)
(4)
(5)
(6)
(7) !#"%$
(8)
(9) &# '(*),+.-/1032547698:<;>=30?4,@ACB.(5DE<FG2IHJ+.=K/10325DMLAN'O/M(5;>8>+.4>2QPR(5D254>425SUTWVX#Y[Z]\_^a`cbedgfihjVX#Yf]klmX#X
(10) npoWqrksto5hjf u,vjltwiYxh^ys*fzklthzhzY {|sm}p}.lmvzh~gY_vzYMkTpYvkTpYo.>*tW `^ystqmmm` * }stmYMf. pt* Y
(11) s*~p~gvjYfjf|s}pvjlmWYXlm>oWYxhilmvj~gYfzqrmoy]qhzTJX#qropqX[npXakxl*f h¡<sto~¢npopqKlmvjX£sm¤?hjlt¤¥str ~gYX#smoW~pf9.YxhiYYo¦hzTpY§mYv hjqrkYf¨ Yy~gYMst]q©hjT¦hjTpYksmfzYlmRkxl*oWks1§*YªqokxvjYsmfzqroprqoWGkxl*f h9KnpoWk«hjql*o ¬ ~gY}YoW~gqropIlt]hzTWY¢kst}Ws*kxqhidQl§*Yv9~gqvjYkxhzYM~¦stvkf¨ Y¢lmphjstqroGrlYv
(12) .lmnpo~pf[Klmv9hzTpqf9}pvjlmprYX¢¨¯®¥o hzTWYmYoWYvjqrkksmfzY ¬±°²´³µ¶².· ¡O]TpYvzYª¸¹»º ¼p½¾¿À¡YYÁgTpqWq©h
(13) fzlmX#Y#3stX#qrqrYfhzTWsth
(14) kxlmofihjq©hjnghzYsmo´¾*¾1à smfzdeX#}ghzlmhzqkstÄsm}p}pvjl1ÁgqXshjql*oªlthzTWYlm}ghjqXstoWYxhilmvj.¨ ÅyÆ5Ç<ÈzÉ
(15) Ê Ë*ÍÌ Yxhilmvjª~gYfzq*oÄ¡WbgÎÏ¡pWnpd5¤Ðsth ¤Ðpnpr.¡gl*}ghzqrX#qrfjshjql*oĨ. Ñó,Ògô ãÀÓ«ÓÔÄÚMÕ×á ÖßNõÄØ.ëiÙèâëiÚ1á Û Ümò«îöÝpÞ1ÔßN÷,àWøÛâázÓã3Þ1ÛâßCä1ÝMåßiã?Ú1ß«æç?ãÀÓiÜ«ÓÛâèeߥémßiá¥çÀê1ëCìêÓÚ1Þ_èí ÓêMç?ßiê1ãÄë¥çÐÓÛ çî]ßiîï1ã3ßÞ1ßNðÓñ?áiòç?ç?ß«Ý. Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex (France) Téléphone : +33 4 92 38 77 77 — Télécopie : +33 4 92 38 77 65.
(16)
(17) |]
(18) ª ª&
(19)
(20)
(21) &# "%$
(22) Ì l*nWf#hjvjsmq©hjlmoWf~ npo }pvjlmWVX9Yy~gYJklmoWkY}ghjql*o ~gYyvMf YMstn kxlghªX#qopqrXstÀ¡]s1§mYknpoWY ~gYX#smoW~gY[hzl*nWfi¤Ð§mYvjf ¤Àhzlmnf]npopqKlmvjX#Y
(23) Yo5hjvzY[YMffzlmX#X#Yxhf¨ Ì l*nWfRhzvstqhzl*oWfR~pnQks*fR~pYfKlmoWkxhzqrlmoWf~gY#kxlph kxl*oWks1§*YfYxhCkvzl*qrfjfjsto5hzYMffznpvNrYf,smvjkf,~ }.YoW~Wsto5hC~gY]skst}smkxqh *¨ Ì lmnWf,l*ghzYoplmof,~gYf,.lmvjopYMf>qogvzqrYnWvzYMf }.lmnpvkY}pvjlmprVX#Y*¨CÎRsmoWf|rYks*f] o vjq *nWY ¬I°*²¢³µ ² · ¡Wl ¢¸´¹¦º ¼p½¾¿À¡WoplmnWf|X9Yh hjlmoWf]Yo §eq~gYoWkY~gYf 3stX#qrrYf 5npqsh hjYqrmopYo5hUnWopY m¨r M[st}p}Wvzl1ÁgqrX#sthzqrlmosmfjf deX#}ghzlmhzq 5npY~gn¢v Mf YMstnl*}ghzqrXstÀ¨ Ê È ZlmoWkY}ghjql*o~gY!v fzYsmngÁ¡pbgÎRÏ ¡ lm}phzqrX9qfjshzqrlmoO¨.
(24)
(25)
(26) !"$#%
(27) &')(*. +.
(28) . N>x
(29) SUTpY#Kl*rl]qoWf hznW~pdUsmfX#lthzqr§shjY~Ieds *nWYf hzqrlmo¯smfzmY~Qed0/pvstokxYSOYYMkxl*X%lm}.Yvshjql*oWst>f Yvz§eqkxYMf kxl*oWkxYvzoWqophzTWYkxl5fihqro bpÎRÏ rlelm}¯opYxhilmvjgf¨9®¥o f nkTIoWYxhilmvjef¡<hzTWY#hzvs1ªk9vzY *nWYf hjf32Kl*v~gYXsmoW~pf4 stvjYvzl*nghzYM~nWfzqrops9fzYxh]lm>klmo5hjsmqopYvjflt 5pÁgY~ksm}Wsmkq©hid*¡e]TpYvjY_YsmkT¢kxl*o5hjstqropYvUklmopoWYk«hfhil9oplg~gYMfUlt hzTWYopYhil*vz<7¨ 6 ~gYX#smoW~ªksto.Y|Knp8 5WrYM~ªed9fzY§*YvstWklmo5hjsmqoWYvf,KlmvjX#qoW
(30) s}WsthzTª.YxhiYYoªq©hfCYoW~g}.lmqro5h oplg~gYMf¨7SUTpYJYMfihstprqf TpX#Yo*hkxl*f hlmhjTpYklmo5hjsmqopYvjfªqrfs¯KnpoWkxhzqrlmo ltqhjfksm}Wsmkq©hid*¡UsmoW~ YJstqrX sth X#qoWqX#:q 9qrop#hzTpY_hjlthstÄkxl5fih]lmhjTpYkxl*o*hstqropYvf¨ SUTpYªfzYxh
(31) lmhjTpYfzYklmo5hjsmqopYvjfksto¯.Ykxl*oWf q~gYvzYM~Qs*fs¢§eqvzhznWsm; 2Kl*vrlmmqksm< 4RopYhil*vzqo ]TpqkT¯hzTWY kxl*X#X
(32) npopqksthzqrlmoWfRstvjY
(33) smkTWqY§mY~Ĩ]®¥oyhzTpqfR}Wst}.YvM¡Y[f hzn~gdhzTpY9~gYfzq*oyltNl*}ghzqrXst,bgÎRÏ lel*}JopYxhilmvjgf mqr§mYoGsklmoWks1§mYqroWkxvjYs*f qropyrqop kl*f h
(34) KnpoWkxhzqrlmo¦smoW~Gs 6|r©¤Àhzlm=¤ 6npopqhjsmvzd¯f Yh[lm|vzY *nWYf hjf¨ TpYo´s kxl*o5hjstqropYvRlmsª*q§*Yokst}Ws*kxqhidqfYf hjsmpqfzTpY~qoIsbgÎÏ lel*}Ä¡.hzTpYfjstX#Y[kst}Ws*kxqhidqfvzYMf Yvz§*Y~¢l*oJhzTWY vjYXstqropqrop }WstvzhlmhjTpYrlelm}Ä¡|fzlGY~glGoWlthklmoWfzqr~pYvhjTpY}pvjlmWYX!lmknpX
(35) nWrsthzqrop hzTWYQkxl*o5hjstqropYvjf ksm}Wsmkq©hjqYMfN}Ws*fzfzqrop_hzTpvjlmnWmTªs*q§*YorqoW.¨ YX#lg~gYhzTWYRfzYxhlmÄkxlmo5hstqropYvfNed#s~gqrvzYMk«hzYM~mvst}WT]TpYvjY hzTWYksm}Wsmkq©hid[lt<YsmkTsmvjk]klmvjvzYMf }.lmoW~WfhzlhjTpYksm}Wsmkq©hid
(36) lt<hzTpYRsmfjf lgkxqshjY]kxlmo5hstqropYvM¨SUTWYoY]lmoprd
(37) TWs1§*Y hz>l 5WoW~]TpqkTª*vjsm}p?T 23smfjfzlekqrsthzYM~#]q©hjTksm}Wsmkq©hjqYMf 4>kstos*kTpqY§mY|sX[nphzq¤ @Wl lm<l*opY|npoWq©hYhiYYoªYMsmkT }Wsmqv]lmoplg~gYMf¨ \Rnpv#lm}phzqrX9:q 9sthzqrlmoöX#le~pY|smfjfzlekqrsthzYMf
(38) hjl¯YsmkTöksm}Wsmkq©hidGs¯kxl*oWks1§*Ykl*f h¨ö®¥o´hjTpY¢}WstvzhzqkxnWrsmv#ksmfzY ]TpYvzYhzTpYkxl*f hqfmqr§mYoed ¬y°m²³µ ² · ¡5]TpYvjYR¸ ¹Gº ¼p½¾x¿Ð¡*Y|q~gYo5hzqKdªsmfjfzd5X#}ghjlthjqrkstrd[hzTpYkxl5fihlthzTWY lm}phzqrX#smopYxhilmvj#]TpYohzTWYoenpX[YBv AlmOoplg~gYfU*vzl|fC¤>hzTWsth|qrf¡gnp}hzl#s9X
(39) nphzqr}prqrkshzqr§mYklmoWf hjsmo*hUrYfjf hzTsto¯ m¨r M¤NedfzlmX#YfzqrX9}WY_3smX9qrrqYMf]ltmvst}pTWf¨,SUTpl*fzYR3stX#qrqrYf|smvzYfzqX#}prdfznpX#X#smvz:q 9YM~s*fKlmrl|Df C ¸ E±&¼ C F SUTpY3stX#qrdlmH G JIKML A DN* smkTpqrY§*YfhzTWYlm}ghjqXstkxl*f h¨ Ì Y Ã C OP=QSRUT ¸ TVOPQXW ¾ R ¡eKlmv Q ¹¢® > SUTpY3stX#qrdIlt ' G [ML PQ3\ Q[¾ R)Z ] G ^I
(40) smkTpqrY§*Yfs3smqv9smfjf deX#}ghzlmhzqksmCst}p}Wvzl1ÁgqrX#sthzqrlmoIvjsthzqr_l 23sth l*vjf h¡<¾mÂr¾M*à 4«¨,SUTpY_§strnpYlt O qf]mqr§mYoed C PcP=Q>\ ¾ RdeJPQfdH\ à QSRcR  OPQR Ea`<b ¾ `<b PcP=Q>\ R'e
(41) QR OP ¾ RUT ¸ T ¾*C SUTpYª3smX9qrrdIlm = G *q§*Yf[sfzlmrnghzqrlmoG]qhzT´sto¦s*fzfzdeX9}phzlthjqrkstkxl*f h gih
(42) 8i& hzlhzTpYlm}ghjqXst f l*nghjql*oKl*v|k¸ j ¼pm l
(43) n*l[sto~*q§*YfUs[3stqrvst}p}Wvzl1ÁgqrX#sthzqrlmoªlmhzTpYvz]qfzYm¨ ¸ E7*¾ C F SUTpY3stX#qrdlm i ogih&pcL A SqNrs smkTWqY§mYfhjTpYlm}ghjqXsmÄkxl*f h¨ Sl9qo5hjYvjYf hzqrop#}pTpYoWlmX#YoWs*fUlgkkxnWv¨\RohzTpYl*opY_TWsto~¡p]TpYo¢¸ hzYo~pfUhzl¼W¡ehzTpY
(44) s*fzfzdeX#}ghzlmhzqkstrrd .Yf h3stX#qrdyhjYoW~pfhzl¢TWs1§mY9stvjmYv_sto~stvjmYvRvjqoW*fstot~ 5WostrdJvjYs*kTpYfhzTWYªf TWsm}Y#lmChzTWYvzqropW¡ÄhzTWsth qf|lm}phzqrX#smO]TpYoJ_¸ E ¼p¨\Ro¢hzTWYlthjTpYvRTWstoW~Ä¡W]TpYoJ¸GhjYoW~pf|hzlJ¾*¡WhjTpY
(45) fzTWst}.YlmhjTpY[s*fzfzdeX#}ghzlmhzqkstrrd lm}phzqrX#smfzlmrnghjql*oQfznW~p~gYopdykTWsmopmYMf|KvjlmX£hjTpY9f hjsmvhjlªhjTpYkxrq 5npY*u¨ 6l*op]qhzThzTpqf_kTWstoWmYm¡.hjTpY9kl*f h 3strf]stpvjnp}ghjd5ds
(46) 3s*k«hjlmv]lt,Ã9sh]hzTWY}l*qo5h¸ E3¾ 23fzY!Y /q*npvzY# 4«¨ x .> y¢ x| v w | x SUTpY}pvzl*prYX lt]X#qopqrX#8q 9qoWJhzTWYkl*f h
(47) lt|sJX[nphzqkxlmX#X#lg~gqhidQopYhil*vz0 @Wl }pvjlmprYX ]qhzTGrqoW¯kl*f h KnpoWkxhzqrlmoWf
(48) qrf
(49) sykxsmfjf qksm,lmopY*¨®ÐUhzTpYkxl*f hKnpoWkxhzqrlmoWf
(50) stvjYªkxlmoe§*YxÁ{¡ zOu vjYsÁpsthzqrlmo¯ksto¯.Yst}W}pqrY~¯smoW~ Xstoed}pvzl*prYXf]TWs1§*YYYoJvjYfzlmr§mYM~¡WfzY}Y | ~Klmvsªf nWvz§*Ydm¨U®¥_o | + ~СstnghjTplmvf|f hznW~gdhzTWY[ks*f Y
(51) ]TpYvjYhzTWY kxl5fihKnpoWkxhzqrlmoWfUsmvzY~gqrfjkxl*o5hzqro5nWlmnWffihjY}qokxvjYsmfzqrop
(52) sto~¡gnWfzqop[rsmvz*YRfjksmY zOu´vzYrstÁgsthzqrlmoWf¡e~gYfjkxvjq.YRsmo strml*vzqhzTWXstprYhjl#mqr§mY_s[rlYvl*npoW~ltÄhjTpYlm}phzqrX#smÄkxl5fihM¨N\×hjYoÄ¡ehjTpY_opYxhilmvjªfznp}p}.lmvzhzqrop
(53) hjTpuY @Wl qf
(54) *q§*YoGsto~¯hzTpYml5stNqf
(55) hztl 5oW~ hjTpYvjlmnghjqoWQsto~IhzTpY¢ksm}Wsmkq©hjqYMflt]hjTpYqropgfhjlsmkTWqY§mYhjTp[Y @l¡ fzYY#Klmv
(56) YxÁpstX#}pr?Y | *¡q ~Ш Yf hzn~gdIs¢}Wvzl*pYX ]TWYvjY#hzTpYklmX#X
(57) nWopqrkshjql*oWf_TWs1§mY#hjlyYvzl*nghzYM~Ql*o s §eqvzhznstopYhil*vzªfznp}p}.lmvzhzYM~edhjTpY}pTedgf qksmlmopY*¨NSUTpYo¢YMsmkT§5qrvzhznWsmqropª.YxhiYYohil#oplg~gYf]ksto¢.Y ,. -. ÔOÔ£Ú
(58) fq.
(59) . JS o o G iG i&. ...... Ring. star of 4−rings. α=0. Star of 3−rings. α=0.290. Star (of 2−rings). α=0.415. qrmnpvjY# rC
(60) RnWs*f q¤Àl*}ghzqrXst.3stX#qrqrYf¨ /. Clique. α=1. qro*hjYvjYf hzqropRKlmv,nWf,smoW~[fzlhzTpY|fznp}p}.lmvzh>KlmvhzTWqrf,§eqrv hjnWsteopYhil*vzqf,~gYoWf Y]smoW~[krs*fzfzqkstgsm}p}pvjl*smkTWYfnWf YM~ ]TpYohzTWYfznp}p}.lmvzhopYhil*vzqrfOhzTWY}pTedgfzqrkst5lmopY 2K]TpqkTqfOlm×hzYo9f }stvf Y 4stvjYNoplmhiY 1kqYo5h¨SUTWqrf}pvjlmprYX ksmoJstf lY[§5qrYY~smBf 5oW~gqropªhjTpY
(61) }pTedgfzqrkstOoWYxhilmvj]TpqkTksmoJsmkTpqrY§*YstrvjY 5npYMfihf|X#qropqX#:q 9qropqhjf mrlmstkxl5fihM¡Wf Y Y | q ~OKlmv|s9}l*deTpYM~gvstÄst}W}pvzl5smkTĨ 6|o¯sthzYvzoshzqr§mY9}pvjlmprYXahjl¢lmnpv_hjTWshstfzlopYY~hzl¢.YX9Yo5hzqrlmopYM~qfhzTpY{]qrop? zÄl5sm~gqrop¢u,vjlmprYX | ~Ш¯SUTWYYMfzfzYo5hzqstU~gq .YvzYoWkxYqrYf9l*o hzTpY¢kxrl*fz Y 23pnghoplmh9Y *nWq§strYo5h 4opl*vzXf#bgÎRÏ tbel*opYxhM¨ lthzT¦lt hzTWYX vzYdl*o#lm}ghjqrkstpvjqoW*f,]TpYvzYUYMsmkT#qrop[qrf,Xs*~gY]ed[s_}WsmqvNlm 5YvjfNklmopoWYk«hjqoW_hzTpY]hil_YoW~p}l*qo5hjf .lthzTs1dgf¨SUTpYbel*opYxhhzTWsthChznWvzoWfhjl
(62) .YqroªKlmvkxYYfjf Yo*hjqrsmrd#qo Ì lmvzhzT 6|X#Yvjqrksp¡5nWfzYfChzTpY}WstqrvfNqroªhzTWY opl*X9qroWsmOX#lg~gY.lthzTs1dgf¡W~gYsmqropª]qhzTJhzTpY3smnphjfRqoJs.Yf hRY .l*v h3smfzTpql*oĨR\Ro¢hzTWYlthjTpYvf q~gYm¡hzTWY bgÎÏ7opl*vzXnf YMfhzTpY}Wsmqv>winfih|l*opYs1dqrohzTpYoWlmX#qostÄX#lg~gYm¡ehjTpYlmhzTpYv]Yqop#nWfzY~l*opdªhzl}pvjY§*Yo5h 3stqrrnpvzYMf¨®¥oks*f YUlmoWYlmhjTpY]rqopgf>3smf¡mstrghzTWY]vzY§mYvfzY 5W.Yvf>lt.hzTWY]vzYX#smqoWqop_rqoWefCstvjYnf YM~hjlkxvjYshjY sto¢stvzhz8q 5kqrsmvzY}prs*kxYX9Yo5hUrqrop<¨ $ | !"% ®¥o±hjTpqf}st}.YvM¡YUsto5hhjlö~gYhzYvzX#qropYQs´l*mqksmbgÎÏ opYxhilmvj´lm
(63) X#qoWqX[npX kxl5fihmqr§mYo s¦fzYxh¢lt vjY 5npYf hjfChzl#smkTWqY§mYm7¨ 6fstoqX#}.lmvzhjsmo*h}WstvzhUltÄhjTpYkl*f hlmsrqoWqrfqhjfU~gY}WldeX#Yo5h¡eYRklmoWfzqr~pYvhzTWsth hzTWYªkxl*f hlt]sl*mqkst>rqoWJKlmrrl|fs¢klmoWks1§mY9qoWkvzYMsmfzqoWKnpok«hzqrlmo¯lmqhjfkst}Ws*kxqhidy]TpqkTI~gY}YoW~pfl*o hzTWYX#sthzYvzqstÀ¨®¥oGbgÎRÏ rlelm}Wf¡O]TWYo sl*mqkst>rqoW]qhzTGsmqr§mYoQvshjY9qfYMfihstprqrfzTpYM~JKvjlmXÍs¢oWle~pY hzlysoplg~gY ¡ÄhzTpY#rlmmqksmfz}Ws*kxY#smfjf qrmopYM~yhjlqhqrf_vjYfzYvj§mYM~¢hzTpvjlmnWmTpl*nghsm>hjTpY#lelm}O¨[SUTpYoÄ¡Klmv_YMsmkT Yf hjsmprqrfzTpY~kxlmoWopYkxhzqrlmoÄ¡hzTpY9]Tpl*Y[}pTedefzqkstopYxhilmvjqrfkTWstvjmYM~]q©hjTJhzTWY[*q§*YoyvshzY*$¨ 6]kkxlmv~gqrophjl hzTWqrf|klmoWfzq~gYvshjql*oÄ¡eYksmoKl*vz*YxhUhzTWYlelm}hzl*}l*l*mdªsmoW~lmoprdkxl*oWfzqr~gYvhzTpYrlm*qrkst<lmopY*¨ T A¯§mYv hjqrkY'f &)(smoW~¢s Æ Ê ! m #" Æ É
(64) Ê % $ qf|vjY}pvjYfzYo5hjY~5dhzTWY
(65) kxl*X9}WYhzY~gqrvzYMk«hjY~¢mvst}WT]qhz? µ . 021 l*oªhzTWY_smvjkfClm3 &4(.
(66) ¨ 5 P &4( R ]qrÄ~gYoWlthzYRhzTWYfzYxhUltO§*YvzhzqkxYMfClm3 &4(ªsmoW~ ksm}Wsmkq©hid9Knpok«hzqrlm+o * -° , / , P &4( R qhjf|fzYxh|lmstvkf¨ µ . 021 lmChzTWY9kst}Ws*kxqhidlmstoIstvk
(67) qf_smfjf nWX9YM~¢hzl¢TWs1§*YhjTpY
(68) Kl*rl]qrop 6 3"t !KÊ " 7 8° . 021±9 Æ Ê + }pvjlm}.YvzhzqrYuf C : 7 qrf]klmoWks1§mY*¡5qroWkvzYMsmfzqop¡ : 7 P ¼ R E ¼9smoW~ 7 P ¾ R E¾ : 7 P A R E<; P A R ¨ SUTpYkxl5fih]lm>s9opYhil*vzqfhzTpYoJf qrX#}pr>d =@?BADCFEHGJILK 7 P * PNM&R)R ¨ ODÆ P " ! !KÊ "RQ@S SiNT GVU P & ( Y * R <$i N '4WYXDZB[]\_^a`DbHZ;Ls G si ML G
(69) =N G gih&Yc L;J G >(*< ph ] X3DN
(70) edf LTgT7* s r s*i G gsh&s * G NJIF=J f r ied LhS i *-h S SiNT GVU P &4( Y * R <ps
(71) Nx=iWkjDlnmo^qpr[ b&Ls G 7
(72) SNsc LKX = ?%ADCFEHG I K 7 P * NP MRcR <pX&3 U
(73) G 7 f r ied;Lh s&2T7* sx3 U >Ls eWs 8 Ls G c h. ÕHtÔÄÕ×Ö.
(74) .
(75)
(76) !"$#%
(77) &')(*. ®¥ohjTpqf,kxlmo5hjYxÁeh¡l*npv,kxlmokxYvjoqfhzl~gYxhjYvjX#qopYhzTWYUkTWYst}.Yf hhzlm}.lmrlm*dhzTWsth>ksto[kstvjvzdsRmqr§mYohzvs1ªkm¨ YkstoKlgkxnWf|lmohil~gq.YvzYo5h]ksmfzYfDC : hzTpYkst}Ws*kxqhzqrYfUksmohstmYsmo5d}l5f qhzqr§mY_§strnpYm¡ f 5¾ Y&Y ¾ Y ¨ : hzTpYkst}Ws*kxqhzqrYfUstvjYkxlmofihjvjsmqopYM~hjl9.Yqro¢s#~gYhzYvzX#qropY~ 5pÁgY~¢fzYxhM¡pf nWkTys* YªkxlmokxYo5hjvjsthzY9lmoQhzTp Y 5Wvf h
(78) ksmfzYm¡stoW~QY#q~gYo5hjq©KdQhzTpYªs*f deX#}ghjlthzqksm>lm}ghjqXstkxl*f hjfKl*vsto 6|r©¤ hzlm=¤ 6,fzYxh_ltCvjY 5npYMfihf]TWYvjY9smvjsthzYMfRsmvzY[Y 5nWsthjlQ * ¨ |oW~gYvhzTpqf_smfjf npX#}ghjql*oWf¡<sKYs*f qrprY[oWYxhilmvj ]qr<.Y_kstrYM~Ks A
(79) j]\_\_^ lnZ m2j ¨ Y_]qrstrX9l5fih]strUs1defCqr~pYo5hzqKdstoed l*fjfzq}ªoWYxhilmvj9]qhzThzTWY ksm}Wsmkq©hidªsmrlgksthzqrlmo¢~gsY 5WoWY~lmoq©hf|stvkf¨ yÊ g !KÊ "» qr§mYo 7 ¡ehzTWYlm}ghjqXstÄkl*f h|lt>p s A<¤ l*fjfzq}opYxhilmvj]qrÄ.Y~gYoplthjY~5d P A R ¨ , ]
(80) Q
(81) x#"
(82) x]7a
(83)
(84)
(85) O ®¥ohjTpYRklmo5hzqroenplmnWfks*f Y*¡mqhqfC.YopYi5kxqstWhzl9f YhChzTWYRksm}Wsmkq©hjqYMf,lthjTpYRsmvjkfCsthNhzTpYqvrl*sm~?2KhzTpYstX#lmnWo*hlt @Wl»}Wsmfjfzqop#hjTpvjlmnp*TJstoystvkD4UqroJstoyl*}ghzqrXstopYxhilmvj<¨SUTpYvzYKlmvjY_hzTpY9kst}smkxqhi) d * ltNsmoJstvk ]qr stfzlvzY}pvjYfzYo5hCqhjfl5sm~#qroªhjTpYknpvjvzYo*hkxlmfo 5Wmnpvshjql*oĨ>SUTpYRksmfzY]TpYvzY 7 P * R E±¸ * \%PNM$ R 23]q©hjT¸ Y $ M 5WÁeYM~ vjYstf4CqfhzTWY
(86) kxsmfjf qksm<lmopY_]TpYvzYhzTWY
(87) kxl5fih]qf|s9qropYsmvUKnpoWkxhzqrlmo¢]q©hjThzTpY
(88) kst}Ws*kxqhidm¨>®¥ohzTpYksmfzY $ E ¼p¡ hzTWYlm}ghjqXstÄfzlmrnghjql*oqfUhzTWYvzY *nWYf hU*vjsm}pT 2?f Y Y & qxo 5W*npvzY_J 4«¨ OÆDP " ! !KÊ "('*) OÆ ÆeÆ +-, x
(89) /. Z102%ZBZ_cL 0 G =(FJ &h4W G cL[ G )T S43q G F * sNd 8 q^I h yÊ g !KÊ "»U Y~gYoWlthzYKl*v|s[§*YvzhzYÁ ² i ¹ 5 P &)( R Y * 1 P ² R E = ?65 E87:9 ;KNADCFEHGnIBK * PNMR ¨ =?)@B A !3Ê Ê 3"Ë +tA 7 P A W ¾ R C P A R C
(90) Ã A 7 P A W ¾ R <CÆ
(91)
(92) ¯> DEBFGFIHBJ zÄlYv
(93) l*npoW~ CYMsmkTG§*YvzhzYxÁ¯TWs*fhzlIf YoW~GsJhzlthstH @Wl lt; A ¾m¡,]TpqkTGvjY 5npqrvzYMf
(94) sh9YMsmf h s¢f Yhlt]stvkf_fihstvzhzqropKvzl*X%hzTsh§mYv hjYxÁ]qhzT kxnWX
(95) npshjY~Ikst}smkxqhidylt A W W ¾#qÀ¨ Y*4¨ * 1 P ² R!Z A W ¾9Kl*v str,§mYv hjYxÁ ² }¨ 6fhzTWYªkxl*f h_KnpoWkxhzqrlmo¯qrfklmoWks1§mY*¡<hzTpYkxl5fihlmhjTpYfzYstvkfqrfsthYMsmf h 7 A ¾ K¨ |}p}.Yv .lmnpoW~ CNq©hklmX#YfKvjlmXhzTpYYÁpstX#}prYlmhjTpYf hjstv]oWYxhilmvj.¡g]TWYvjY_skYo5hzvst§*YvzhzYÁªvzYMkxPYqr§mWYMf]stR oW~fzYoW~pf hzTWYvzY *nWYf hjfhzlsm<hjTpYlthjTpYv!f 23fzY!Y /q*npvjY
(96) Kl*v]hzTpY_YÁgsmX#}pY]qhzT AtE l*4«¨ L . ! B . yQ 7
(97) . A. B 4. 4. 4. 4. C 4. 4 4 D c. 4 E. arc of Kn of non−zero capacity routing of requests from D. qrmnpvjYCNSUTpYf hjstv]oWYxhilmvj.¨ ®¥oyhjTpY
(98) rlYv.lmnpo~yltHzOYX#Xs + ¡<Y|winWf hhst*Y
(99) qro*hjls*kkxl*npo5h|hzTWY>5Wvfih_stvkltNYMsmkTJ}shzTQfihstvzhzqrop KvjlmXs9§*YvzhzYxÁ¨Ynghq>YsmkT§mYv hjYxÁTsmf|s9TpqrmTy~gYmvjYYm¡gqh]qrOYoplmh|sY 1ªkxqrYo5hs*fUhzTpYkl*f h]KnpoWkxhzqrlmo¢qrf /. ÔOÔ£Ú
(100) fq.
(101) JS o o G iG i&. xk l*oWks1§*Ym¡ghjTpYoJhzTpY[o5nWX
(102) .YvlmN§mYv hjqrkYf]]qhzTJTWq*T~gY*vzYYTWsmf|hzlª.Y[fzXstrsmoW~¢hzTWYofzlmX#Y
(103) s*~p~gqhzqrlmoWsm ksm}Wsmkq©hid9]qr.YvjY 5npqrvzYM~¨/qrvjf hCYvjYXstvj[hzTWsth¡eqostoªl*}ghzqrXst&A<¤l*fjfzq}opYhil*vz<¡mhzTpYvzYRYxÁgqrf h P A R §mYv hjqrkYfhzTsh|qrogKlmvjX P A R §*YvzhzqkxYf]sml*op#~gq}shzTfUlt>YopthjT¢sth]YMsmf h|Ãp¨ G p(*<B 3sNT GVU ML>
(104) T x&'=I G
(105) -fB_T
(106) G {p G h <CÆ
(107)
(108) ¯ DEBFGFIHBJ benW}p}l5f Y*¡CKl*v#qoWf hjsmoWkxY*¡Cqroösmo¦l*}ghzqrXst]opYhil*vz¯lt_ksm}Wsmkq©hi d *¡Chil¯~gqfihjqok«h~gqr}WshjTWf . sto ~ d stvjY
(109) .lthzTInWfzY~hzl¢ksmvzvjdy}s @Wl ltsthrYs*fi h
(110) j¼.YxhiYYoQs¢f l*npvkxY[smoW~s~gYMfihjqoWsthzqrlmoÄX¨ zÄYh v 7E¾ Y rà 4x¡gY_hjTpY_KnpoWkxhzqrlmohzTWsth|Y 5nWsmrf_ _lmohjTpYstvkflt NstoW~#lthjTpYvj]qf Y*¡pstoW~kxl*oWf q~gYv UP R 2×Kl* * E * \
(111) UP RW
(112) P R sto~ * E * \
(113) UP RW
(114) P R s ¨ lthjT *,smoW~ * ,smvzpY A<¤ l5fzfzq}QopYxhilmvjgf d sto~l*}ghzqrXstOfzqokxY 7 qf|kxd l*oWks1§*Ym¨ L yÊ g !KÊ "» ~gYoWlthzYMfhzTpYoenpX[Yv]lt>§mYv hjqrkYf]q©hjTy~gY*vzYYsth|X9l5fih ¨ i P A R E!
(115) Ã A 7 P A R Ji0 ]d S3 A ] FsNT GVU L E ( K <>Jp&h4W G <CÆ
(116)
(117) ¯ ML> G sKML>Nr=I G p
(118) H3 P A R YT >J
(119) E ( K Z A W P A R h DEBFGFIHBJ A W §*YvzhzqkxYMfNltO~pYmvjYYRshrYs*fih \ ¾qroW~gnWkYs
(120) kxl*f hlmOshYMsmf h P A W R)P \ ¾ R 7 P ¾ R E A ¾ 23s*f zOYX#Xs
(121) fzTpl¦hjTWshChzTp;Y @Wl qrfCqo5hzYmvst 4«¨ 6f zÄYX#Xs + *q§*Yf A à A 7 A ¡ P YW Ts1§mY R)P P A W \ R R C à A 7 P A R ¡pfzl9q" P A R E à A 7 P A R hjTpYo E ( K Z A W P A R ¨ P R C P L R Æ
(122) ¯gB $I 6f 7 P A R E ; P A R 2Ked~gsY 5opq©hjql*o 4«¡qro[smolm}phzqrX#sm l5fzfzqr}Ä#¡ P A R E@; P A R stoW~fzl E ( K E A \ ; PA R¨ Sl[qrX#}pvzl§*YhjTpYrlYv.lmnWoW~¡ehzTWYstvjmnpX#Yo5hU]qrÄ.Yhzlf }Wqh]hzTpY}shzTfUqo5hzl9hil[}stvzhjf¡pstoqopqhzqst }Wsmv h]TWqrkT kxl*oWfzqrf hjfqo hjTp?Y 5Wvfihstvk¢ltYs*kTö}shzT stoW~öqroW~gnWkYfs kst}smkxqhidGKnWoWk«hjql*@o *$t¡|smoW~öhzTWY vjYXstqropqrop}Wsmv h]TpqkTkxl*oWf qf hjfRqoyhjTpY9lthzTWYv_st1 vkfRlt,hzTWY[}WsthzTWfsto~JqroW~gnWkYfsksm}Wsmkq©hidKnpok«hzqrlmo * ¨ SUTpYqoWq©hjqrsm.}stvzh 2 *%$q4CqrffznWkTªhjTWshKlmvUstoed ² ¡ * ² A ¾m¡5]TpqrYRhzTpYvjYXstqropqrop
(123) }Wsmv hUstrl|fstrX#l*f h hzl
(124) }Yv Kl*vzX #s l*fjfzq}Ä¡*qo~gYYM4~ * qrogKl*vzXstrrd[strrl$ |P f,R Ys*Z kT§mW YvzhzYÁ
(125) hjlqopKlmvjX smWhzTpYRlthjTpYvfNf hjstvzhzqrop_KvjlmX fzlmX#Yf npf Yh_lm 5£]Tpl5f Y#fz8q 9Y9qfshX#l5fihqhjf~gYmvjYYm¨9®¥o¯lmv~gYvhjl¢kst}ghjnpvjY[hjTpl*fzY9hil}pvjlm}.YvzhzqrYfY ~giY 5WopsY RnWs*f q¤ l5fzfzqr}ªopYxhilmvjgf¨ &')(. *,+-.0/2143657.0.0/98. ®¥o
(126) l*vj~pYvÄhjl~pYvjq§*Ys|rlYvO.lmnWoW~Yf hznW~pds|vjYsÁgY~oWYxhilmvj.¡MhjTWsh>Yksm: h& ] ¨>®¥ogKlmvjXstrd s Rnsmfzq©¤ l*fjf qr}yopYhil*vzqrfhzTWY9fznp}.Yvj}l5f qhzqrlmoJlmNhilksm}Wsmkq©hidKnpoWkxhzqrlmoWf * $ sto~i*; t¡ * $ qf_f nWkTJhzTWsth > Y§*Yvjd §mYv hjYxÁGTWs1§*Ysmo´l*nghz*lmqropIkst}Ws*kxqhid lt A W ¾ysmoW~ *< smrl|f[hzl¯}.YvzKlmvjX f l*X#Y 23rsmvz*Yq4[f Yhlt pvjl*s*~pks*fihz¤Àrq*Y[l*}YvjsthzqrlmoWf¨ Yª]qrf YYrsthzYvhzTWsth RnWsmfzq©¤ l*fjfzq}IopYxhilmvjgfkxl5fihX#lmvjY#hzTWsmo l*fjf qr} opYhil*vzgf¨ /qrvjf h|Y~giY 5WopYs = ]?> G D *Nr C ODÆ P " ! !KÊ "A@ ) =ÀCÈ B Ê pËmp + S P & ( Y * R sNT GVU <p 8N =1 ED %j [B.GFB[]\LmSieT GVU L>X * sNd. LhS i * 8LT7X'K G Ls G f LTT is;cL = N<S i U ; r st U}G iDJI0
(127) SXh&;cL fB_ TJ
(128) SN is MLui
(129) h G >N<S iSL G
(130) J> U h. Æ
(131) ¯gB $ Ì lthjYhjTWshM¡eqos =Àq¤ vzl5sm~pksmf h¡hjTpYkst}Ws*kxqhik d *ksmosthzYvzoshzqr§mYd9.YfzYYosmf!s @l Kvzl*X smo Tede}lmhzTpYhzqkstWnpopq*nWYf YoW~gYvC§mYv hjYxÁhjlhzTWYf qropgfNed[nWf qrophjTpYfzYxhClm<fzlmnWvjkYfNs*f,qo5hjYvjX9YM~gqstvjd§mYv hjqrkYf¨ ODÆ P " ! !KÊ "IH*)KJ OW !È LÊ M !NM + S P &)( Y * R SiNT GVU <
(132) 8N} P A YCOrY = R)] : h& ] t L$ G !(*< *. $ SN ;* h& s J
(133) ] *BE * $ \ *; ] * $1 P ² R Z A W ¾ Ls G
(134) 8d². h. ÕHtÔÄÕ×Ö.
(135)
(136)
(137) !"$#%
(138) &')(*. . . ] *; BE = 5 *; 9 T7 G *< 9 < u * sNdHLh s?ML = ?] > G q rN* h *;
(139) WNr $sN O = ?] > G q rN* h ! " & P A YEO*Y = R P A CY OrY = R . yÊ g KÊ » Y_~pYoplmhzY . hjTpYX#qoWqX[npXkl*f hlms ¤ RnWsmfzq¤ l5fzfzq}opYxhilmvj9KlmvUhzTWY kxl5fihUKnpok«hzqrlmo 7 ¨ p BMLp
(140) A ] FsNT GVU <K 8 #& P A YK Y A W ¾ W R h <CÆ
(141)
(142) ¯ P A RUZ & P A YK Y A W ¾ W R DEBFGFIHBJ ®¥oIx s A<¤ l*fjf qr}opYhil*vz<¡Äsm §mYv hjqrkYf ² lt~pYmvjYY#rYfjfRhzTWsmo qoW~pnWkxYªs = 7 ¤Ðpvjl*sm~Wksmf h ]qhzT = 7 Z A W ¾ W U¨ zÄYhhjTpY * 9 7 .YRhjTpY_opYYM~gY~ksm}Wsmkq©hid9Kl*vYMsmkT = 7 ¤À1 Wvzl5sm~pksmf hstoW>~ *$hzTpY_opYY~gYM~ ksm}Wsmkq©hidªKlmv]hjTp!Y @Wl f Yo5h|hzTpvjlmnWmThzTpYqvRopYqrmTe.lmvfU]TpqrkT¢TWs*fUhzlY * ² A ¾_Kl*vstr ² ¨SUTpYo hzTWYkxl*f h]lt,Xs A<¤ l5fzfzq}opYxhilmvjqf]X#lmvjYhjTWst
(143) o & P A YE Y A W ¾ W R $¨ P R Z W L &'. 57.,5 - *,+- .0/ 1 3 57.0. /)8 O ÆDP " ! !KÊ " , ;i _dXJ N
(144) G s'N) <K p G P Y R N G i'N[' h. G &}< X j%ZD\Lm L < * dr i o p SN Ls G r s} G ')( 7 G . /pvjlmX hjTpqfª~gsY 5opq©hjql*oÄ¡Y¢fzs1d¯hjTWshsQ§mYv hjYxÁG]qhzT opl stvk~gqvjYkxhzYM~GhjlIqh02KWnghªY§*Yo5hznWsmrdGfzlmX#Y rYs1§eqoW[qh4Uqf]sxG q ¨ <CÆ
(145)
(146) ¯ Q J G K(*<! P A YCOrY = R)] : h& ] T [X&3 { YT7 G K J = ] W G q rN* > G J>s
(147) U3 G G p h > W G q rN* H< f G Ls G N hJ^I[ ;Ls G s h DEBFGFIHBJ ZlmoWfzqr~pYv &4( Y * sto¢lm}ghjqXsmJ RnWs*f q¤ l5fzfzqr}opYhil*vzstoW~ * $rY *; s~pYkxl*X#}l5f qhzqrlmo¢ltY*s*f ~gYMfzkvzqrYM~¢qoJÎRsY 5opq©hjPql*o ¨ R d~psY 5Wopqhzqrlm{o C * E * 9 \ * 9 d \  \ * P 9 ]TWYR vjYYsmkT¢KnWoWk«hjql*io * 9 qrfs =Àq¤ vjl*s*~pks*fihM¨RbeqroWkxY9edy~gsY 5WoWq©hjql*oJhzTWY[ksm}Wsmkq©hid * lt+ s RnWsmfzq¤ l5fzfzq}¢opYhil*vzopYY~pflmoWdhzlY[hzTWY fznpX%lt O =À¤ vjl*sm~Wksmf hjf¡.Y9oplthjY9hzTWsth_smo5id *%$ \ O * 9 9 ¡ÄKlmv BE¾ Y ÃU O ¡Äqfs RnWs*f q¤ l5fzfzqr}Ä¡f +l *qf_s kxl*oe§mYxÁ
(148) klmX[pqoshzqrlmo[lthzTpY RnWs*f q¤ l5fzfzqr}W3f *%$ O * ¨,beqokxYhzTpY]kl*f hKnWoWk«hjql*o9qf>kxl*oWks1§*Ym¡YklmoWknW~pY hzTsh¡ehjTpYvjY_YxÁgqfihf]stolm}ghjqXst RnWs*f q¤ l*fjf qr} P\ & ( Y * R ¡p]TpYvjY * qrf O hjqX#YMfUhzTpYfjstX#Y =À¤ vjl*sm~Wksmf h¨ Y opYÁ5hklmoWfzq~gYv]fznWkTys[}stvzhzqkxnpstvUlm}phzqrX#sm P A YCOrY = R ¤ RnWsmfzq¤ l5fzfzq}O¨ 6RfzfznpX#Y_hzTWsth]hzTpYnWoW~gqrvzYMk«hzYM~*vjsm}pT fznp}p}.lmvzhzqropªhjTp>Y @Wlg *< ~gleYfRoplmhRqroW~gnWkY[sKl*vzYMfihM¡WhjTpYohzTpYvzY[YxÁgqfihf
(149) 3j»¼fznWkTyhzTshfzlmX#Y[§mYvzhzY>Á vjYkxYq§*Yf_[s @Wl
(150) ªsml*op¢shYMsmf h_hil¢~gqfihjqoWkxh
(151) ~gqr}WshjTW f 9smoW~ d ¨ zOYxh UP R 2×Kl* v ;E¾ Y *Ã 4«¡Ä.Y#hzTWY KnpoWkxhzqrlmo[hzTWsth,Y 5nWstf l*ohjTpY]stvkflt sto~
(152) lthjTpYvj]qrfzYm¡smoW~[klmoWfzq~gYJv *SE * $ \ *; \
(153) P RW
(154) UP d R sto~ * E * $ *;
(155)
(156) '¨ lthjiT * Y * stvjsY RnWsmfzq©¤ l*fjfzq}Wf¡psto~ *_qrf|hzTpYqvX#YstoO¡fzlW¡s*f ¬ qf]kxlmoks1§mY*¡e\ Ykxl*oW\ kxrnWU~gPY_hjd TWRsW 'h * UstP oW+~ R * smvzY_stf l#l*}ghzqrXst3 RnWs*f q¤ l5fzfzqr}Wf¨ L Yopl Y§1smnshzY9hjTpYªkxl5fihlt]stoIlm}phzqrX#sm RnWs*f q¤ l5fzfzqr}JlthzTpYªsml§*Y
(157) Kl*vzX¢¨ Ì lthzY#hjTWsh
(158) fzqroWkxY ¬ qfUqoWkvzYMsmfzqoW[Yksto¢smfjf nWX9YhjTWshUhzTWYkst}smkxqhidªkxl*vzvjYfz}.lmoW~pfChzl9hjTpYkst}smkxqhidopYMkxYfjfjstvjd#hzl#pvjl*sm~Wksmf h fzlmX#Y_qogKl*vzXsthzqrlmohzl =C§*YvzhzqkxYMfnf qrops9KlmvjYf h¨ <CÆ
(159)
(160) ¯ Q]Q JpX&3 ML P A YEO*Y = R] : h& ] 8 & P A YCO*Y = R U<K
(161) H 8 5 " 7 O 7 P! O R\ = 5 # Ã. P R = 5 9 b 9 9 d ! DEBFGFIHBJ Y|klmoWfzqr~pYvNsto#l*}ghzqrXst &4( Y * RnWsmfzq©¤ l*fjfzq}[]q©hj T * E@* $ *< N]TWYvj'Y *; ~gYfjkxvjqrYMfNsKlmvjYf h $ smfqto zOYX#Xsy W¨ 6RfzfznpX#YhjTWshRP lmopYeopR l|f * ¡hzTpYo *$qfsmX#l5fihR\klmX#}prYxhjYrd~gYhzYvzX#qropY~¡.qroW~gYYM~ hzTWYl*opdklmoWf hzvstqrol*o *$qrfhjTWsnh * $1 P ² R Z A W ¾NKlmv,smo5d ² ¹ 5¨,beqroWkxY ¬ qfklmoWks1§mY,hjTpY]kTpYsm}YMfiYh RnWsmfzq¤ l*fjfzq}qflmghstqropY~
(162) edkTplel*fzqop *$ ² Y&% E A ¾Klmv,stoedstvkNrYs1§eqrop ² f nkThzTsnh * ² Y&% qfXstÁeqrX
(163) nWX¨ Ì lmhzYhzTWsthhjTpYvjYXs1d9YxÁgqrf hfzY§*Yvst.P f nWkTR stvkfNW WnghqrohjTpqrfUksmfzYstrWhjTpY_kTplmqkxYMfCstvjY|Y P *nWq§RstrYo5hM¡5smoW~lmoWY ksmoªkxl*X9}WnghzYhzTpYkxl*f hClmOstoekd Rnsmfzq©¤ l*fjf qr}#f qrX#}pd#rlelmeqoWsh * ¨ Ykxl*oWf q~gYvClmoWY]hzvjYY|lmhzTpYKlmvjYf h. ÔOÔ£Ú
(164) fq.
(165) JS o o G iG i&. ]qhzTvjlelth5¨,®ÐOhzTpYvzYRYxÁgqrf hjfUs
(166) §mYvzhzYÁk2?~gqrf hzqroWkxhKvjlmX hzTWYRvjlelth4C]qhzT~pYmvjYYmvjYshjYvChzTWsmog¡5lmoWYRksmo shzhjs*kT#smltqhjff npphzvjYYfC~gqvjYkxhzrd
(167) hjlhzTWY|vzlelmh¡mYÁpkxY}phzY~#l*opY|]qhzTªXstÁeqrX
(168) nWX *; Y Klmvstr f¨,SUTpqrf lm}.Yvshjql*oy~gYkvzYMsmfzYfhzTWY
(169) kxl5fihRfzqroWkxY_hjTpY[kst}Ws*kxqhidKnpoWkxhzqrlmo~gYMkxvjYs*f YMfUq©,lmoWY
(170) kxl*oWP f q~gYv]R hzTWsthRsksm}Wsmkq©hid KnpoWkxhzqrlm+o *|qfmvjYshjYvhzTWsmos9ksm}Wsmkq©hi4d *.qi¡gnp}hzl#s
(171) }.YvjX
(172) nghshjql*oÄ¡ * W * Z x¼ 23fzYuY /q*npvzY + 4x¨>®¥olmv~gYv root (0,3ns). root (0,7ns). (0, 3ns). (0,3ns) (0, 4ns). A. D (n−1,ns). D. (0,ns). (0, 3ns). (0,ns). B. (n−1,0). (n−1,0). (0,ns). C. (n−1,ns) (0,ns). (0,ns). (n−1,0). (n−1,0). (n−1,ns). C (n−1,ns). (n−1,ns) (n−1,3ns). (n−1,3ns) (n−1,0). B. A. (n−1,ns). (n−1,0) (0,ns). (n−1,0). (n−1,0) (n−1,0). (n−1,0). (n−1,0). (n−1,0). q*npvjY + C^¢l§eqoWJsJf nWghzvjYYhjlyhzTWYvjl5lmh[~gYMkxvjYsmfzYfhjTpYkl*f h¡>Ys*kT stvk M qfst.YrY~G]q©hjTGsJkxl*np}prY P * $ PeMR Y *; PeMRcR ¨ hzlªfzqrX9}WqKdªhjTpYkxl*npo5hzqropY_]qrOopY§*YvUhjsmmY_qro*hjlªsmkkxlmnWo*hUhjTpYksm}Wsmkq©hid)* $ Klmv|stvkfUrYs1§eqrop9hzTpYvjlelthM¨ Zlmof q~gYvspvstokT]qhzT¯YopthjT ¥¡hjTpYl5sm~QlmoQhzTpYªsmvjk#sth hjs*kTpY~hzlhjTpYvzlelmh_qf O ¡hjTpYrl*sm~QlthzTWY stvk9sh~gqrf hjsmoWkxY j¼ªKvjlmXahjTpY#vzlelmh5q uf A W ¾ \ P W R O Z 5P " W \ ¾ R O ¨9belhzTpY9hjlthjsmNkxl5fih_qo~gnWkxYM~ ed#hzTpY_pvstokTª qrfUsthrYs*fih 7 P O5Rf \ = 5 7 P O R E à 7 P O R\ = 5 7 P O R ¨NbeqroWkxYhjTpqrf pE vstoK kTkxl*o*hstqroWE f K fzqopgf¡eYR}Ws1d P à 7 P O R\ = 5 " 7 P O RcR }YvUfzqrop<7¨ zOYx h ; = P OrY = R E b 5 9 d 9 9 d 1
(173) .YhzTpYX#qropqrX
(174) npX kxl5fih}.Yv9f qroplmUs¢WvjsmoWkTÄ¡ÄhjTpYkl*f h_lm|stoedJpvstoWkT¯]qhzT Ufzqopgfqf_hjTpYoGsth
(175) YMsmf h ; = OrY = ¡.f qroWkxYhzTpYvzYsmvzY =f qropgf¡sto~fzqroWkxY_hjTpY
(176) kxl5fih|lm>hzTp Y Rnsmfzq©¤ l*fjf qr}qf]hjTpY
(177) fznpXlm>hzTpY
(178) kl*f h lthzTWYWP vjsmoWR kTpYf¡gY_klmoWkn~gYhzTWsth & P A YEO*Y = RUZ = >; = P O*Y = R ¨ L ÆeÊ Æ
(179) Q' i>¬ P A R E A W ¾ W P A R Ã 7 P! ¬ P A RcR\ = 55 # " 7 P ¬ P A R)R P A RHZ ¬ P A R 5 9 b 9 _E ( K ! DEBFGFIHBJ 6|}p}Wdeqrop} zÄYX9Xs stoW~yZlmvjlmrstvjd * _Y_TWs1§*Y Ã 7 P ! R\ = 55 # " 7 P R P A RUZ P A W ¾ W R 5 9 9 9 b( d " " ! st}W}pdeqrop#q©h|]qhzT P A R &¡ zÄYX#X#sª[*q§*YfhzTpYvjYfznph¨ L Æ
(180) ¯gB $9Ì lmhzY[hzTWsthKl*vzX[npslmSUTpYl*vzYX Mksmo.Y#klmX#}pnghjY~QqoI}.lmrd5oWlmX#qrsmhzqrX9Y*¡ÄX#lmvjYl§*Yvq lmoW7 Y5 #]" qfz TpYfKl*v]Yf hzqrX#sthzYMf¡pl*opYksmoKl*v]rsmvz*YR§strnpYMf ! nf 7 Y_5 hjTpY_3smkxh]hzTWsth 75 $ 7 P ¬ P A R ² R ² C = 5 9 9 9 7 P ¬ P A R ² R*C 75 7 P ¬ P A R ² R ¨ d /. %. &'. 5"8 57.!
(181) " . 5#)+ 9/ 5$ .. Ê MCÊ ! !3Ê ". Q. = PA R C PA W. ¾ R b '&()& ( " . ( E( 1 K (1 7 *A ( Q W p d +. ÕHtÔÄÕ×Ö.
(182)
(183)
(184) !"$#%
(185) &')(*. DEBFGFIHBJ 6 f l*nghjql*o¢]TpYvjY_hzTpY~pq*vjsm}pT¢lt>oplmog=¤ 9Yvzlkst}Ws*kxqhidstvkfUqf]Kl*vzX#Y~edkdgkxrYf]lmhjTpY
(186) fjstX#Y zf q89YklmopopYMk«hjY~Ged l*opY§*YvzhzYxÁGfzYYX#f[hjlQ.YysJmlelg~¦klmoWf hzvjnWkxhzqrlmoĨ ®¥o¦hzTpqf#f l*nghjql*oÄ¡NvjlmnghjqoWnWfzqoW YrYX#Yo*hstvjd}shzTf|qfnpoWq 5npY
(187) smoW~JfzlhzTWY[ksm}Wsmkq©hidlt,YMsmkTJstvkqf]hjTpY[fjstX#Y
(188) smoW~¢hzTWYoyhjTpY[kl*f hlt,hjTpqrf opYhil*vzIksto .YYMsmfzqrdIYf hzqrX#sthzYM~ C9rYxh Q3\ ¾ª.YªhjTpYªrYopmhzTGlm]YsmkTGkdgkxrY023fznp}p}.l*fzYªhjTWshXA W ¾ªqrf X
(189) nW©hjq}prY_lt Q 4«¡ehjTpYohzTWYrl*s*~ªl*oYMsmkTkdgkxrYRqfUnpopqKlmvjXstoW~qfUY 5nWst.hjXl A Q>WFQP=Q\ ¾ R'e Ãg¨,SUTpYoYMsmkT kxdgkYkl*f hjf PQB\ ¾ R 7 ( P A Q;W?QPQ \ ( ¾ E R'( e à R K smoW~smfChzTpYRoenpX
(190) .YvltOkxdgkY|qf P A W ¾ R'e
(191) Q ¡thzTWY|hzlmhjsm.kl*f hClthjTpqrf opYhil*vzqf P A W ¾ R 1 ( 7 * A QpW d 1 + U¨ /q*npvjY#*q§*Yf]fzlmX#Y_YxÁpstX#}prYflt( hzTWqrf|krs*fzflm>fzlmrnghzqrlmof¨>®Ð 7 P * R E@* · ]q©hjT9¼ C ¸ C ¾m¡1hjTpY]kxl*f h>qrfX#qoWqXste]TpYo¾ e ¸ E PQ\ ¾ RP ¾ W ( " ( " R ¡tq?¨ Ym¨Klmv Q E ¾ e ¸ W ¾*¨ 6f Q\ ¾RqfhzTpY_rYopmhzTlmYMsmkTkdekY*¡ Q TWs*fChjl[.Y_mvjYsthzYvChzTWsmoQ _sto~hzTWd YoªhjTpY_lm}ghjqXsm<klmoWf hzvjnWkxhzqrlmo ltOhzTWsthhide}.Ym¡eq©¸ Z ¾ e Ãp¡*q fhzTpY_ " fi· hstv· opYx hilmvj 23str< kxdgkxrYfltÄrYoWthzT¢r 4x¨>SUTWYoªhjTpYX9qropqrXstkxl5fihltÄhjTpqrf eqo~lmklmoWf hzvjnWk«hjql*oqf " · · A 1 · \ ; P A 1 · R ¨ L A. A 10. 10. 1. 1 A. B. 1. 7. 7. E. B. 1. E. B 1. C. 1. 7. 7. 7. 10. 10. 7. 1. 1. 1 1. 1. 1. 1 1. 1. E. D. 1. 1 C. D. C. 1. D. 10. G2. G4. G3 arc with non−zero capcity routing of a request. q*npvjY9C#&âstoW~ &&CkxlmofihjvznWkxhzqrlmoWf_nf qropykxdgkxrYfltfjstX#YrYopmhzTĨ & Clm}phzqrX#smCkxl*oWf hzvjnWk«hjql*oKl*v ,¨ Ì l Y|lmoWd#kxl*X9}stvjY|lmnpvl*npoW~]TWYo 7 A qrflthjTpY|Kl*vzX A · ]qhzT¸¦¹¯º ¼ Y ¾x¿Ð¡tKl*vChjTpqrfYfihjnW~gd Tpl §1smvzqrYfhjTpYsY 1ªkxqrYokxdlms9pvstoWkTO¨ P R /. 7 PA R E A. &'N& 3 57.0. /)8 $ ! 5
(192) 57. / Q <ÊeÉ
(193) Æ Ê 3 "Ë TpYohjTpYªkxl5fihKnpoWkxhzqrlmo¯qrf 7 ° A ³µ A · Y9TWs1§mY d E BE ( KHK 1
(194) E _E ( fzqX#}prYstostrdefzqf#lt d 1
(195) fzTpl|f9hjTWshªhjTpYJ§strnpY ! $ Klmv]TpqkT. ¬ · P A R d 1
(196) ¡ hzTWYJX#qopqrX
(197) nWX!qfªshzhjsmqopYM~ qroWkxvjYs*f YJ]TWYo ¸ ~gYMkxvjYs*f Y* ¨ /pl*v¸ ¹Íº `!#" d P%$d R Y ¾¿_hzTpYQX9qropqrX
(198) npX qrf¢g¡sth hstqropY~±Klmv ! E ¾'&Kl*v ¸ ¹Gº ¼p à Y ¼pÂml
(199) nt¿À¡ehjTpYX#qopqrX
(200) nWXqf +* 1 ¡WshzhjstqropYM~ªKl*v E Ã9stoW~smfUrlmoW#s*fhzTpY_X#qropqX[npX qfUoplthsth hjsm`!q#"oWYd ~$d)Klm( v ! E,p¡g]TpqkTTst}p}.YoWf]Kd lmv|d ¸ ( ¼p Ã-&Wsto~fz! l9lmoÄ¡WSstWY# _mqr§mYMfhzTpY_qro*hjYvj§stfUlt ¸GsmoW~qhjfkxlmvjvjYfz}l*oW~gqrop[l*}ghzqrXst§strnpY ! $m¨ 8' . MMNÆ Ê 3"Ë Y[ksmo~glhjTpY#fzsmX9Y[kxlmX#}pnphjshjql*o¢KlmvRhzTpY[np}p}.Yvl*npoW~JsmoW~ 5Wo~¢hzTpY9.Yf hfz8q 9Ylt,hjTpY9kdgkxrYYopthjT 2 Q>\ ¾q4s*kkxl*vj~pqop[hzl9hjTpY§strnpYlt>¸C¨NSstprY
(201) [mqr§mYMfChjTpYqro*hjYvj§stfUlt¸GKlmv 5Wvf hU§smnpYMfUlt Q ¨. ÔOÔ£Ú
(202) fq. KHK. E.
(203) . JS o o G iG i&. $ ¸ º ¼pÂml
(204) n  Y ¾x¿ ! º ¼p Ãp¾N Y ¼W lrn  ¿ º ¼p *Ãp¾N Y ¼W Ãg¾N ¿ + º ¼pÂârà l*lU Y ¼W 5Ãg¾N ¿ º ¼pÂâÃg¾M¼] Y ¼W *à lrlU ¿ º ¼pÂr¾  Y ¼W Ãp¾¼] ¿ º ¼pÂrq¾ l ] Y ¼W¾  ¿ º ¼pÂr%¾  Y ¼W¾ l] ¿ ¨¨¨ ¨¨¨ SsmpY# *C,®¥o*hjYvj§stflm>¸ Klmv]]TpqkThjTpY§strnpY ! $ X#qropqX#q:9YMf d 1 ¨ ¸ Q º ¼p ¾ lU Y ¾x¿ º ¼pÂâà *¼] Y ¼W q¾ lU ¿ º ¼pÂâÃmà  Y ¼W à m¼] ¿ + º ¼pÂrD¾ n#] Y ¼W Ã*à  ¿ º ¼pÂrq¾ l Y ¼WÂq¾ n ] ¿ º ¼pÂr%¾  Y ¼W¾ l ¿ º ¼pÂr¾mq¾ n] Y ¼WÂ+¾  ¿ º ¼pÂr¾^¼ lU Y ¼W¾*D¾ n] ¿ ¨¨¨ ¨¨¨ SstWYC,®¥o5hjYvj§1smrflm>¸¯Kl*v]]TpqkThjTpY§strnpY Q X#qropqrX9:q 9YMf b '&()& ( " ( 1 ( Q · ¨. Ê NÊ Æ Ë Ê O !KÊ " A Æ 1 ÊeÉ
(205) Æ Ê "OË 6f ¬ P A R E A · \ ; P A · R hjTpYlYv.lmnpoW~qf 5 E K E K · Ã = 5 " · ! \ A 1 · & & _E ( K ; PA 1 · R \ b ! sto~ªhjTpYnp}p}.Yv|.lmnWoW~¡p]TpqkT¢qrf P A W ¾ R b & ( & ( " ( 1 ( * A QKW ( E ( d 1 K + · ¡gqf]rYfjfhzTWsmo E K E K Q>\ ¾ A 1 · ( b Q Q · \ ; P A 1 · R lthjTylt,hzTWYfzY
(206) X#qoWqX[npX%~glªoplmh~gY}YoW~JlmU A q©U A qfRrsmvz*YYopl*npmTO¨RbelW¡KlmvYs*kTy§strnpY
(207) lmC¸C¡.hzTWY smfzdeX#}ghzlmhzqkstvshjql#.YxhiYYo¢hzTpYnp}W}YvRsto~hjTpYrlYv]l*npoW~¢qf]l*npoW~gYM~¢eds#kxl*oWfihsto5h¨ Ì npX#Yvzqksm stostrdefzqfqr?o /q*npvzY[qroW~gqkshjYfhjTWsh]hjTpqrf|vjsthzqrl9qfUrYfjfhzTWsmoI *¨ 1g¨ [ U
(208) . ®¥o#hzTWqrfC}Wst}.YvNY]TWs1§*Yqroe§mYMfihjq5shzYM~#sto#qX#}.lmvzhjsmo*hCfz}.Ykxqst.ks*f YUltopYhil*vz[~gYfzq*o#]q©hjTªkxlmoks1§mY]kl*f hjf¨ SUTpY_vjYfznp©hflmghstqropY~f Tpl±hzTWsthhjTpY_mYopYvst<f Tst}.YRlmOhzTWYl*}ghzqrXst<opYhil*vz#§stvjqYMfUf qrmop8q 5ksto5hzrd]q©hjT hzTWYhide}.Yltkxlmoks1§eq©hid9YRf hznW~gd*¨>®¥oªhzYvzXfltÄopYhil*vz#~gYMf qrmoÄ¡5hjTpqrfvjYfznphqrX9}smk«hfNhjTpYnpoW~gYvjf hjsmoW~gqrop lt_X
(209) nkTöX#l*vzY¢hjTWstoöhzTWYQbgÎÏ opYxhilmvjgf¨ \kxl*npvf Yys¯oWsthznpvst 5npYMfihjql*o klmoWkYvjoWf#lthjTpYvªhid5}.Yfªlt ~gYX#smoW~pfRhzTstoQsm¤Àhzlt¤¥strOvjY 5npYMfihf¡smoW~ylthjTpYvhide}.YfRltkl*f hjfhzTWsmonpopqKlmvjX%kxl5fihfl§*YvstrhjTpY9Y~g*Yf¨ /pnWv hjTpYvUqroWf qrmT5hUqohzTWsth 5WY~ªlmnp~ª*vzYMshjd#TpY}hzTpYhzYYMkxl*X9X[npopqksthzqrlmoªl*}YvjsthzlmvfCsmoW~ªlmhzTpYv]smk«hjlmvf qrohjTpY_hzvstof }.lmvzhjsthzqrlmoqroW~gnfihjvzdhjlTWs1§mY_s9X#lmvjYiY 1ªkxqrYo5h]X#smoWst*YX#Yo5h]lthzTWYqrv]vzYMf l*npvjkYf¨ =. % GM. ÕHtÔÄÕ×Ö.
(210) * .
(211)
(212) !"$#%
(213) &')(*. 1.12 asympotical ratio. 1.1. (upper bound)/(lower bound). 1.08. 1.06. 1.04. 1.02. 1. 0.98 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. α. q*npvjYfC 6fzd5X#}ghjlthjqrkstÄvshjql 2Knp}W}Yv|l*npoW~&4 23lYvU.lmnpoW~4Usmkklmv~gqrop
(214) hjlª¸C¨ w B.| ] |r s~Î
(215) ¨ qYoWf hzlgk<¡b<¨<ZTWlm}pvsp¡\[¨ pop p<¡.smoW~ZR¨ ¤9¨Sfzsmq?¨]^¢qropqX[npX kxl5fihkst}Ws*kxqhidqroWfihstrrsthzqrlmo¢Kl*v X
(216) nphzqkxl*X#X9lg~gqhidoWYxhilmvj @Wl|f¨ Ji3
(217) G )I G XX^I ¡ *C # ¡p ¨ |â~ 8¨ vzlgke X prYvM¡W\[2¨ pop p<¡Wsto~ zC¨ 6
(218) ¨ l*rfzYd*¨NÎYMf qrmoWqopu,vjqr§1sthzY!zÄqropY Ì Yxhilmvjef¡< # ¨ | + ~
(219)
(220) I¨ _smpvzYsmoW~Q^ ¨O^¢qoWlmngÁ> ¨ zOsmvz*Y9bgkstrpY zu {]YrstÁpshzqrlmof|Kl*v_^¢qropqrX
(221) npX Zl*f h^¢nW©hjqrklmX#X#le~pq©hid /l u,vjlmprYXf
(222) ]q©hjT¦b5hzY}G®¥oWkxvjYs*f qropQZl5fiK h /WnpoWk«hjql*oWf9stoW~¦Zl*X9}WnghjsthzqrlmoWsmC{]Yfznphjf¨JSOYMkTpopqksm {]Y}.lmvzh e ¡ zOst.lmvshjlmqrvzY_?^ 6Rbg®«2¡ |opqr§mYvjfzqh u>stvjqr f Wf¡ /pvstoWkYm¡ # W¨ |
(223) ~>6¨\Rnpl*vzl*nÄ¡eu¨W^JstTpYdm¡gstoW ~ p¨ ¤¥u¨
(224) Rqrsm?7¨ 6»f npvj§mYd#ltsm*lmvjq©hjTpXfNKl*v]kxlmoe§*YxÁ#X
(225) nphzqkxl*X9X#lg~gqhi3d @Wl }pvjlmprYXf¨
(226) S iI^i i&H is > h ¡p}stmYMf ML ¡et*mp¨ |â ~
(227) ^¯¨1u,vzd5h 9m*¨ zst*vjsmopmqsto_~gYklmX#}.l*fzq©hjql*oKlmvmYoWYvstmf hzY}
(228) kxl5fih>f qropmrYN}WsthzToWYxhilmvjR~gYMf qrmoĨ5SOYMkTpopqksm {]Y}.lmvzh|S]{]®iS 6]¤i?^ 6,S¤¥mm51¤ \_bg + ¡5{]ld5st<®¥oWf hzqhznghjYlt>SOYMkTpoplmrlm*dm¡pbeY~gqfzTÄ¡t**p¨ | ~>6¨bgkTpvjq wi§*YvM¡Mu¨beYdeX#lmnWv¡sto~u¨ qropeYv¨*SUTpYCvjqoW|l5sm~gqrop]}pvjlmWYX¨ S h G f>"K<s G i= Ji
(229) s ¡O m^ 2i 4Cr W¡. # ¨ /. ÔOÔ£Ú
(230) fq.
(231) Unité de recherche INRIA Sophia Antipolis 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France) Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France) Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Rocquencourt : Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France). Éditeur INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France).
(232). . ISSN 0249-6399.
(233)
Documents relatifs
In infantile Pompe disease patients, the glycogen storage diffusely affects brainstem motor and sensory neurons, and the whole spinal cord sensory neurons, interneurons, and
De ce point de vue, il est possible d’affirmer que la mission est accomplie : les projets de renouvellement urbain (GPV et ORU) élaborés depuis 1998 dans une centaine de villes
cosinus (en bleu à gauche) et d’une droite (en noir à droite) sur les données simulées pour 4 années à une température de 45°C, avec un bruit de fond interne réduit de 100,
Florence CARRÉ ~ Réoccupations funéraires de sépultures collectives néolithiques dans la boucle du
2 Vue plus en détails dans le chapitre 1... 2 phénomène d’agrégation des protéines amyloïdes en fibres et d’autres facteurs impor- tants doivent être pris en compte comme
In this chapter, we prove an a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the boundaries for
Revue française d’héraldique et de sigillographie – Études en ligne – 2020-10 © Société française d’héraldique et de sigillographie, Paris,
Dans ce cas, comme les coulées du Bras de Sainte-Suzanne appartiennent au massif de La Montagne daté à plus de 2 Ma (McDougall, 1971), l’ensemble des coulées pahoehoe