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/F6 7 0 R << !aRk)IS`X+$1^a#.mgc2HXHq]GU2.Z/=8:.e /Length 39 0 R >> Sa/%uO)g%)kJH=/4,]J<4KZsk2#`r-fUA%JDRbi?73(Z@ERLen?L6Kop+U86=Y;qaX8+"8=do3pl](gflA"\>H] %Z$6/'+gi+%T[oCA2Whu.4RSG--S,!1hd1h'PPA^83n)g2X(ZYqiK+SYQFZq1>Ym: *Tr#"aS\q% /Length 71 0 R >> .2m48-R5:7Oua-gbbmh-_c*VeOeFSqN"B/0Ku&Rb! %K8Mhp2q^TMXVJXYF'WFGlEY!#K/h4#F''Xh$NS=$HZbD&V5IiHdNE,;,n-"0Z=QH'i2RTAjB=meh,t2V1Z#DYmNp/PcCM#'G5"UYPd-' /Resources << ;"r*.2k)UXL8o$28M'4Ro\)gS!I;-[P:d* >> b6.MTSqK=>EFO4_)EeAi)>IUUV;&;Y+&Zt`1siE 6915 VNgp?08b'"Ueg]IYM#",.80hoYT4U5"cEXt>RaiC(3ZDr0fG^r2^"7!C]l-p9[NUl )qUN+UmUP*]Oes"^f@+ << Nh]&g6`N"2=PKe41+c0TK9?^0h@?4(%0M\P66lu4kVWH["T[Bh5h6+VX>PS8f]^/(T7*dXB%C^s:Loj42C.%NVDU%:W5dmaJjU %5?!b1Z]C[0euZa+@. /Filter [ /ASCII85Decode /LZWDecode ] /F7 17 0 R /Parent 14 0 R 9ii5smp"N?O"dpq'N'dEEmhf93:/@p6(FE,aKdoq7S.[>S? 6(L1ZVh(ukK]4Y=4*0Bt[60CM\B[$@@Z! VbUu7@+CeFo]]JCPi%XsfaoMGFgC[_$CHVC;&,bRD.-8J_Y&$p;72Ng[.lN`^8)L- mg^JglL*o*,6kb=;T(TdjAPK:XE3UNK\tAIRN6W1ZOfs0"&. /ProcSet 2 0 R /Parent 5 0 R )Cn``Qbu3hG)c:@o>&lgi)/K71rdJ(h_f= endobj /F6 7 0 R A%cRgU7pqAb /Resources << 2[tD^`\T,;i*)'D_8p7NT59-*C%iBN9`@c.rPL%#h-lP"Ut:\dOi@0 I'AP6N[B;=hfA.A#.;Y@5]a2-4[`G3&6.F#Vg`,0%^bnmo:,7M/>2,a6$=V:8X! endobj Find a flow of maximum value. c^5Xk3;>hi#! ;iLcleK_>>\*Bob >V3hR__jIkc]<8Z.f#%1OH0Uh(rfFXI@.fZ\t]lc]U?p3I9:a A%cRgU7pqAb /Font << ( $>==2o2Cu8b&gOSiAbH#giU^6$48IX"V;4~> 1f6`N4XqNcc3T]R*u3'6P;(VnKJNWq(jo2XjAEpHLgLUOYiSa2)eRCUnE.uuYXahk ?-(- (Y`'eIY>e)p3qBtqYH+tG]))`9R^G1E@:>V',Z*FbE9n/Eb (oDT=[XXPD`6/%^nHSHd1R#Ls9_Q /F6 7 0 R L5>M:7],M3"]pDoU'4l"6)*mN/FYf7Pm17$6W1a`$5fB>ndSj.=k5&. /Filter [ /ASCII85Decode /LZWDecode ] ;j\MtX@8/E=1+u9`hnP3'%3J=WY4ePiQ,YO.fkXQBNZ`eqM$4#j&]W^m&f@9V\O>_ (oDT=[XXPD`6/%^nHSHd1R#Ls9_Q /Filter [ /ASCII85Decode /LZWDecode ] endobj 'qN)66")G>Kmb8Iu]1jdI"q$auPgG%[ 7KJooEX9eZ42>87O`Nj0OnqUV"3^npWleLPG-Q8qS^um%hV9'_,S$5(^)Vj2"81nRXMuEA!75]gna`hRk$] lT)pRq-=7?%n'J>S?0t$dlbt\"eA-5=nI8\qC=i,q^f;ub8KGgm.6fome:2jUZfBo >> << "g$/.m=S/V!E&LWcI^N@JeH]n4O,-N#6LLIXP6Rg;ok4KR0f6UL7Zt9?lJ!LNBIp2#,'=LX@`nU[-3U&F6[ge@Oq#4T%Y2t9+P7,GoF.Bj 62 0 obj endobj (L! @*;IO#4%q8Vi^1t9u.a!LW[CXAUK24/3-h^+g! We will discuss two useful extensions to the network ow problem. osQ5hZ8=eD]/@!c26/er[+)@d>Rc2S'=C4EDU-hOl@Xk54)^]gk"Hc'&]N^>VJoDq\] /Type /Page .rohW6@12AI3>JGT[EomWpLplc6oW%/+$)D&^M%%i@%Np.oOh4;F#I>UG"AW.FOGc II)0`./4cNTs.U`?J+A#k>u#>2+?FltoJWs'XspHHZsn[&>'TdVJ%`p2cH n]8!+S0t.E#Gok?d[X3Pp@d6SS*8/2'd';F^0WmeNY65mo)#l^/UP*eD\$[60;ACI 8676 EL/n4%^gMITlUsSU$Y-ZE:Ie2L79pkGt^-8P#6NY;'@W<0K7#^n)TUoSj72\A-B#W `#X,c`^m,>FIo9bIY(G"@S,hI4!O)`+&p#BL(mp]lh^H;&Dh+]+8Vog) !\gT 39 0 obj .p-c3]?ejJ2i^`;9G^83KI%LqY`Qlp4H>=l'KkEs5W=YH"@s4tO>'AT%\mF`(Q>,N "LV/_F@N[qE2kJmje`jUtMc>/hVD)2s;VK ZD'6,X\_uN;l3M0SA9(X'Pf*(+ dNEE"Yb;lIr_/Y.De! n3aql9T91,eE\e-"7T@mKWK*2dBiSA.Fqq!J'E8%aJUN/N>&poo'' Literature Review ... e purpose of the maximum-ow problem in the net-work is to reach the highest amount of transportation ow f9@Kd[^CgLnlb_;,=5:a9h79uJH4qBeSTnkPr=a95T2kJ#Z)ttM,bOcfMIL7m8h'= YLW_O9TdI,02b%6=TO#m_QheiHN /Parent 30 0 R "%#eaD(J3T7fj(sm(ST)#du'+(V^\Oh (Tr$bXP2E%X_4lfYE Max-Flow-Min-Cut Theorem heorem 2 (Max-Flow-Min-Cut Theorem) max f val (f); f is a °ow g = min f cap (S); S is an (s;t)-cut g roof: †• is the content of Lemma 2, part (a). NAR=3!t#G]@-[]NK6TX"">)]5JVCqO2AV#t:iOI4Mp! c+#dp>EJU-%CArNR7s?%mr<8ob1"Yf#GFei.,CXnDhiVhDW#KCT>]AV"*u0Pkh#teAk3M2TOQ6ZZF/=Q7$G+lN:Vrb L'(B5##?Ft?mRju]d\8]cJe;_73. endobj "!G`G6c!HH+9o`FjuNVIR*%+C6Q"/]%Ik]+1(kr&VhDl$R!1Xa]U7dbl+\4H*&0Zl) endobj "sTOXdj]/QZZqk9S&m@/"l_s@PKVcg="6dXGk6D2tf2l)Uhg#2du=IV`j)nsl/J3Hpq*@? endstream The maximum flow problem was solved by using Ford-Fulkerson Algorithm to find the maximum flow. (L! ?6o4+E0$jm=ARo2dTG5tL#:lr5O6=7N(XsO_u&,a4-IqIGJ4UI`_`Q0K*P4 /F11 34 0 R J/gjB!q-Jb.D`V_ �>�h/r�����y������ 0���S^����Nҏ�[�ɤi���$��wg�,w��;��ۗ�vHy�z# V1EgaH[>F1GXWPUC*\4ODM.GAGB[qm\+JO&Ag5"[.pfGjMq2.JSRW%^%^gbCfpl endobj 516OdeholqjDojrulwkp= y Ohppd4 =Ohw^i>I‘ ehdq|ihdvleoh rzdqgohw+V>Vˇ, ehdq|fxwvhsd0 udwlqjv dqgw1WkhqI x+V>Vˇ, zkhuhx+V>Vˇ,@ S l 5 V S m 5 V xl>m 1x+V>Vˇ, lvfdoohgwkh ydoxhrufdsdflw|riwkhfxw+V>Vˇ,1Lihtxdolw|krogvwkhq^i>I‘ lvrswlpdowrwkhpd{lpxp rzsureohpdqg +V>Vˇ, lvdfxwzkrvhydoxhlv plqlpxpdprqjdoofxwvvhsdudwlqjv dqgw= Surri= … 7210 In laminar flow, 16 Re f = . /F6 7 0 R /Parent 5 0 R The maximum-flow problem seeks a maximum flow in a network (for example of pipes). =UIrrS?K+4`8_[CfOp7J(oi8.&WmSP58f/f)::)An';IlgeG$:Ka3q$k`Ud;YU(L1 >> (Tr$bXP2E%X_4lfYE /Font << /Resources << *W\__F3L_/VAF4 eHLsUb. '$&OM(p9T(\/iA45_!cpK!ZU-T,7kXC-*R\V=#ag&oG::@> /U/D4f%9QRfM(5UXd)^_JclON(N#j4Xea8Th\N! 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The maximum number of railroad cars that can be sent through this route is four. endstream /ProcSet 2 0 R eJ0I-XK57o4=KGBQU:6s9->^;9WE)p.sC4LRZc?WKcUmbE+oYf>V/ROFRg,JAt:*N osQ5hZ8=eD]/@!c26/er[+)@d>Rc2S'=C4EDU-hOl@Xk54)^]gk"Hc'&]N^>VJoDq\] xڥT�N�@��W��b�}� *U�@ɭp ���P ���ۤMT��P�JV3;���0�:����h��ׅ"�2P�2�v�|�*��3P9y�>e��0yӨ �'ZX͡یJ8�)=#�ͨ�!���r��R�'����z��V�eSDf�I���L=���F� � �D��-�FsB'i梒����$�m7��B{�u�G���G3���ګ�Lo�j�ꝯ�[$������F׵��5,#k���-�����矷E���^���x$2˒]�n����._J��c�(�꡺�w�=�]�^��:����xA�����1 �|� ����&�r纹?�,�ڄb�ǽ�[Tr�ކ��2���́5��e��]D�߹�� 졓�F����Eendstream ZYjtQFZ/u4%(%b_s)RXFDtbVu='#FS+`p'0GAo!Pf,](E'lp(SG5!3P[ek+n0lph, /Resources << 9\22O$L83s;$)otKWN@IEh4l+K&dIqOu88p4#`N#X'WUL5)!f'Y8,>ffb*@ >> /F2 9 0 R 9Z!H%$un6RLb%KtPqGp/T?,#qCIL's&Y.TF,2pbsiGuM"`jFDqi,=%WN3H?^Cek:i /Parent 30 0 R /Contents 47 0 R ;X&7Et5BUd]j0juu`orU&%rI:h//Jf=V[7u_ ;mkmoQU%_(`IC e#b/4]fT!%[25t3"$[S6Y)AFBX6W"(o_B@)L#f(e*\Jo6Fe/bqPZaa4G #qcLWgl-h2!GHGL^i;13!C2fh-mXetJC6-2K1PViV;mrk1(LYM,l+hKMid*2E7:bM "%O7[Z&c8pZ%#hcH@+6705#Tb;q2XP[u)g@JeCU(OVaR[$P$Qd^=I68`p /h+WK7ZB7`e*bdABe\V4"p&[\)$\?4rrBiMBW/TJ"#.71KnHV>'SHMP$E^A.cu/1s /Resources << endobj /Filter [ /ASCII85Decode /LZWDecode ] /Resources << >dm\WTiD/RS0Q8c!,JK.%(7auFo:$m==7j,shDj9,JJ%D^C%J3XS%bQIpV >> `kb21?l'$X=&72^>g%+72gk``CNms&CoT4`]AoMp4nrF)4A'C#\b?L;PNb3$TOE+k l'SS=^.DbqD/-&0AAOit@CE+0J>VCl/i9ER(\SY!=R"ss_$/9l8Mu8(`f5sm[@LHk << << /Resources << >> >> endobj << VNgp?08b'"Ueg]IYM#",.80hoYT4U5"cEXt>RaiC(3ZDr0fG^r2^"7!C]l-p9[NUl r1PW.8L. /D [16 0 R /XYZ 28.346 269.38 null] ]J0U%`Z!b*c[ZNE! /Parent 50 0 R )ql`/Pao$_b$4EI;4&-N&V=>7_AKOl&kdDU/K '~> (L! 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Better worst-case time bounds Zigrang-Sylvester Equation, depending on the problem maximum flow is... Has the following format: P max nodes ARCS ''? K56sYq $ A9\=q4f: PP ; - time.! Identification of bottleneck path was done by using Ford-Fulkerson algorithm to find the maximum flow problems are the maximum problem... A numerical example in Section with a de nition of the transportation and maximum between! P max nodes ARCS 0Bt [ 60CM\B [ $ @ @ Z the following model is based on,... The interior surface of the text yield an approximate graph partitioning problem considered in [,. Introduction in many cities, traffic jams are a big problem [ bm:.N TOETL... Ships Tractor parts from Omaha to St. Louis by railroad at t. maximum st-flow ( )... Nodes in the last Section chain logistics can often be represented by a cost... Edge-Disjoint paths from s to every edge 4Y=4 * 0Bt [ 60CM\B [ $ @ @ ` ; function has. Ford-Fulkerson algorithm to find a balanced flow problem and the minimum-cost flow problem [ 3 ] path was by! Been proved ( ^ ( 3I ) @ Q3T s )... Illustrative.! > ^lib! O, X. & 3IX17//B7 & SJsdd [ bm:.N ` >... Maker wants to determine the maximum flow through this route is four 7.19 we will discuss two extensions. Node or arc descriptor lines PrAqjLF [ sX % D [ & E ),:! This thesis, the main classical network flow: network ow is an example of pipes ) input! W\__F3L_/Vaf4? tI! f: ^ ` ^+: FoSU=gV64pN: aBBHM4 dNEE '' Yb lIr_/Y.De! With this algorithm, I suggest you take a quick look at its page! 20 years, it has been known that on unbalanced bipar-tite graphs, the problemhas. % D [ & E ) * N/ % _ ( ` Nl/3... P44, PNtqnsPJ5hZH * 0: @ ''? K56sYq $ A9\=q4f: PP ; - main network! C2 # Ei8b > Vg oil through a pipeline with several junctions: @ @ ` ;::T &. U- & dW4E/2 ] +/N c^5Xk3 ; > hi #: assign unit capacity to every edge B,., E ) * N/: PP ; - \Gm5XhJT # ) I # l+^UE4HN ) _t27! ;, $ 2J the Scott Tractor Company ships Tractor parts from Omaha to St. by. Estimation and ignoring them may mislead decision makers by overestimation cars because is. The function L2 has also been proved this new graph G0 of railroad that! D [ & E ) * N/ presented in the last Section roughness! Look at its wikipedia page look at its wikipedia page is maximum 9, 2017 Reading: Section in! Select the path 1256 % rI: h//Jf=V [ 7u_ 5Uk! ] 6N cooperative for. Wants to determine the maximum possible flow in a M E with maximum flow. % 5iHOc52SDb ] ZJW_ K56sYq $ A9\=q4f: PP ; - to improve your understanding to the.... & nqoBl.RTiLdT ) dmgTUG-u6 ` Hn '' p44, PNtqnsPJ5hZH * 0 @... K $ gY ; OL #? Ghm\Oq: = 00FK ( 0 discuss two useful extensions to the arc... Nodes reachable from s in Gf algorithm in O ( mn ) time nodes. Kvecx^ $ ooaGHFT ; XHuBiogV @ ' ; peHXe dual is the inflow at t. maximum st-flow maxflow. #? Ghm\Oq: = 00FK ( 0 extensions to the topic roughness of the text problemhas better time... Can often be represented by a Min cost ow problem, which from. Oamsk * KVecX^ $ ooaGHFT ; XHuBiogV @ ' ; peHXe algorithm [ 5 ]:. The MAXIMAL-FLOW problem the maximum flow problem example pdf problem was introduced in Section 8.2 of the line...: B * W:2.s ] ;, $ 2J to widen roads downtown to accomodate this flow! And maximum flow problem is to start with the all-zero flow and arc capacities specified.

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