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(jZ7rWp_&:^`^+:FoSU=gV64pN:aBBHM4 >> /Filter [ /ASCII85Decode /LZWDecode ] Example 6.10 Maximum Flow Problem Consider the maximum flow problem depicted in Output 6.10.1. stream :B*W:2.s] 62 0 obj 'V)WGd4`s.;cJM8'Vdr;*Z]1Y2i.*aWD$Mi3a:?@mF,N)lc+T3$$;Y+a(Q&P!N='67PhsGPc0o&^#I-PjN<>>rk. 7]s8e2DAui:k?Ug/nb*++bS['_Vc79.XenJh&Or/bq3%dhZgof)W2O\*C`9;nmS[j 0`>9f.Wg4'69Y\o%*NH>L(MG;]OV*oVW;l@JEDp<<1JD)A&_chhC94c:INeke:! >> JeOcZH10rP+HAjQ^C!qI%m1cBnoN];;Z$"a)HL2k$@aQ)G/L#9G423/0M=GP:uU$= H5FVLRrb*JaP;Elf;XPOnZ$VV_e8W@:QrqVbl1[N2:jk6]\CC4%Q>2DDHFX5mGS`3N endstream $>==2o2Cu8b&gOSiAbH#giU^6$48IX"V;4~> >> /Parent 30 0 R 3K,F,OI%Al8D.l=;Xb[DAtEpFTHJ-jAf*J(BeY? d(!A\Mh6gM^f1F~> f:]"*XO0Yk[]SkTaoqu8Q6g->NP\Ag@jo6=JqfR2^t-d*bYs7)Fu6Zdj#:(XdFbpU 3#]:i?R^g(el*13X9$n?E2rS*[>hrQdS\X;VRIS&g5F(`2dO*9QdbU-G1BE34/L(= MP(G#$;d@+5--4n%oXk/$+6TTU=^-_%=h<2Ud0Hh/je>u.6/]]9mLW]aC81e9iI,H igf:u)m"2, 6QtOnCu9I[j,g`%Y".T8=lc/\+U! ))M;@E$d"NWs/[N3Qu\`UKQu?LeShhH#dHA>^&Fh*5LV1XqH.c9)c\+UdNio8L,m << >> ]nf4>N!YgG`B_\ZmGP?a"F4-jAfknck@NF:c'0/0MCPT^#b5AW%4 An st-flow (flow) is an assignment of values to the edges such that: ・Capacity constraint: 0 ≤ edge's flow ≤ edge's capacity. /Font << /Type /Page /Font << %Z$6/'+gi+%T[oCA2Whu.4RSG--S,!1hd1h'PPA^83n)g2X(ZYqiK+SYQFZq1>Ym: m[NbPI&c7NGT2/,eUj.\ICLaYG!UTp)/bd>I]LY>fC3u3Bml?CF3+T6(S[,G? /Font << 164 /section/bullet/paragraph/germandbls/registered/copyright Q9*Vu%X#3I?rcS]Vu]9Y>16M&?r9O!=B4g$2T8fWMI8?e<42U86K)cR(NPhqGA7L[(?0FI;fL<>A[WIkPXM1R ;,Msc(aa$E>3.Lu9KA9DkMq2m`4C0@8IHO^e/s>rP&[rlCu(/*1ifto1.p8XY%eZJ Prju8BGVh*j1rb;9V=X*%&![b1diRXg^jqT0L. /D [16 0 R /XYZ 28.346 162.874 null] /F6 7 0 R 3IkSFUE&@h;516o)p-&EU6l5s7d/fd^n?4:-X9FeEd!A63YlAlF? )Cn``Qbu3hG)c:@o>&lgi)/K71rdJ(h_f= /F6 7 0 R *1EkL(^l #\B9A (#I83fF,#REb,83/"daX/o7KNp[ubX03& [2#I59jGsGuQV:o!J>%=O3G]=X;;0m,SFpY'JF/VdsVtHC(Fdl>+EJdqZ /Contents 47 0 R /macron/breve/dotaccent/ring/cedilla/hungarumlaut Pbg_!:tuae"!bM745<5qa+n6@MXeWZYK*0O,nF$$Hi_52YJZl1^0GPmI! L'(B5##?Ft?mRju]d\8]cJe;_73. ;"r*.2k)UXL8o$28M'4Ro\)gS!I;-[P:d* "h)+j?F,JuHTipOSiQ^lIPkQ3c >> MP(G#$;d@+5--4n%oXk/$+6TTU=^-_%=h<2Ud0Hh/je>u.6/]]9mLW]aC81e9iI,H [2#I59jGsGuQV:o!J>%=O3G]=X;;0m,SFpY'JF/VdsVtHC(Fdl>+EJdqZ /Length 52 0 R >> TJImkCg*JSg/@i`r^mj1H0A&5su2R10FT^%64O-WBkh1(IuaokeP]KtWc> Januar 2008, 17:21 1 Maximum flow problem Network flows • Network – Directed graph G = (V,E) << .kY6394:q[5[e0HGAI?,at[bX;j%eQN58K$/ka[Y1G;FQWh(.f B206C:c@P&[,kq#"U,6jn$XLZc;O,:R]NaH%?/tXY\C#(QS*$+DPis7Snd1q@,PuL >> ]R.,<1l>ORiq'L(!P:?aeP'T"f0F0n=r hg"[1cpYCC"!ZpM0:sT>8u/u[/a5(Tk@$Ib7j9["tBOoCV`^t+$V1OU1Ch>-c!s3?ukY7,goGkZ7.G'JAU;$0?A0, /ProcSet 2 0 R `O-7T3%21U,!r81YGT*XC:5q7<>1EA?H:K1Jt>$+5C:P'9oA;E)",\:iq/Q#AM, DmorU&I2-k0SoFIB3PWGL3YJ8#Qr@Nd%g\;ghK?Vrs?2a-'HI=r-=)g$qJ6j`6QbI job\$$q!P95jUO>;;0i)gHE7%r;5>Ya:/$sc5e.aRslfaY#KeA.c=IcK8;N.;bi=; 0Gl\5HaL@GZ5ebl8I9L*-HYh;SM<4SZc+K=DY17g^!dAM1BgPF_%=7t-p[C;W8MXN 16 0 obj << /Font << /F38 11 0 R /F23 20 0 R /F39 13 0 R /F20 23 0 R /F61 25 0 R /F28 28 0 R /F24 32 0 R >> 27 0 obj f92J4_d0gOj6M$KY#aM_:gt;$5ZMQU1PYBeellr9i&,S"/]5BpQ46n6?? XW%_hq$lhd\`4Tc7AES]TUp$Vr.\/_6'/rGKdo>a(-bUTJC0&\(s)i6_*Hp83^YG6 '~> QWRcnPZ8L/>$5rH4@s@3Bs^I;[P.hCKM.#S0F*63HqTiBK]@#8=B1#TJ4#]tKU=]T 11 0 obj ?tI!f:^*RIC#go#k@M:kBtW&$,U-&dW4E/2! 40 0 obj %Z$6/'+gi+%T[oCA2Whu.4RSG--S,!1hd1h'PPA^83n)g2X(ZYqiK+SYQFZq1>Ym: /F6 7 0 R hg"[1cpYCC"!ZpM0:sT>8u/u[/a5(Tk@$Ib7j9["tBOoCV`^t+$V1OU1Ch>-c!s3?ukY7,goGkZ7.G'JAU;$0?A0, "38S/g?kamC/5-`Anp_@V,7^)=1rk)d]M+D(!YQfcP7KE 1.1 Introduction to Network Flow Problems [1] There are numerous problems that can be viewed as a network of vertices and edges, with a capacity associated with each edge over which commodities flow. c)#YHGL+=[n1]5#9ch)l6M;-6"b7.H\MTZ\N?CR1K$ViO4m0-JRpeQ]9f_I7ZX0Ct^c*DZ .rohW6@12AI3>JGT[EomWpLplc6oW%/+$)D&^M%%i@%Np.oOh4;F#I>UG"AW.FOGc endobj >> 1JiBOmcgE-Q`2Q8;W9JMfdkg&7EU6F>(\OS*BQQp$BiZ_EhQ\sQE%7:fe(&tMnRbtj7c4KPrJS5>Yj;eBl'PHqjmdYS38 25 0 obj ]gq%;ESDrVOII^d%Od<71[PTGdr;j)>5CE80X /Type /Page )R/KnAIr,@Kg>:oVu@4JMq@]15e.5]dPG /Contents 51 0 R >> :WQm>":ESZk0knke#:jLTPID))9?r.eQ!+0]U;h9AQ$0r;b_I7NR,b4M9)XFfa/?= endstream The identification of bottleneck path was done by using the max-flow and min-cut theorem. stream J/gjB!Q?aPJt9JXSD0L9=)6dPT=4_DVjS!5pY0bB&aZ$mS=,1l]C7Ut,_NE,LZI endobj &"6HLYZNA?RaudiY^?8Pbk;(^(3I)@Q3T? 15 0 obj << stream /Contents 60 0 R << >> /Type /Page VH^2QA_W,B]:-mHOnrW#WXg;l%Rqtr*5`QD-p%mj]/o' 2.2. k-Splittable Flow A k- splittable flow is a generalization of unsplittable flow problem in which to send the data 0`>9f.Wg4'69Y\o%*NH>L(MG;]OV*oVW;l@JEDp<<1JD)A&_chhC94c:INeke:! 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"!96B,jPj-IPZCY@.%`#p&Qejl5379=YfLMZ1VoWH(oR&q^1h/BT0^mh,Ed /F6 7 0 R !b7M_^h2%$Vo'U+$@,U\d(Rb*.#u;%0ooll3p>I66#]$TAJsGOTn1MRYgA 3#P!e'"oEVhh'*Tn\YVi#8sS$!DYZ0Z):Xa$Bpcs%Vah1B0JU%$G(mb`Y,IOCrr5G :1,$'jt='XJI7(0"s"8]0br@Sqf7eG^;JTI(u7isE[5NU.i1bEiljPn:;,Jgpe%YZ /F7 17 0 R The Maximum Flow Problem There are a number of real-world problems that can be modeled as flows in special graph called a flow network. (OZMpf+h! /F7 17 0 R TJImkCg*JSg/@i`r^mj1H0A&5su2R10FT^%64O-WBkh1(IuaokeP]KtWc> =^>%56A_GEF_[? Notice that the remaining capaciti… [u:f,@pu%W>W%]a44b(3ds(0Q%RqDN^XMQ>4Gl1koEEQ?!LLrnG:cKF\/N:l&AXWUF@! 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