9rN$G"SMq\CoeM]m7M>\ OXFB/^O,XO_Vr9;#Ja"K&eA*e\`%V:6cOQjHm(lCia\@`> >> ))M;@E$d"NWs/[N3Qu\`UKQu?LeShhH#dHA>^&Fh*5LV1XqH.c9)c\+UdNio8L,m @5cO'3Y1NU/I;?\i6AU=*0ADG&^Vf0q&P\935RLBo5d:K+EI*;)\\o4EVVZ#Y6jH< KJRo\361FYkS+D6KXNRp[!4k[N^3Zd3=I-G_\nDU'b8R;0gmBaN? )P=#QCM,=;B3FNNVMtF-)e# a1cE[:bF35]0_K6YUXUT^#>o#*2QK50$T*&YdbC#!TVVo26P"7N!CkCjLg0K(rA6@ SlMI!5;#(R_a8E"'cUm*]*D_>*]diMX_V,6T.UGg8&$3LhJf=/rs6Ot[=c7t>RXJ]mO4qeh=1BmC`B[^ni& 'NQ9s>F*$hSJ%E,_Q.us\U?V5Rk9lflFI_*/BSY-HfAm4 YjuL?#8I%*=qAirq>4]-]p#c3]#Loq3Fa:G?n!-^b95sdB8R@d8d"(G"W[o6p >> f9@Kd[^CgLnlb_;,=5:a9h79uJH4qBeSTnkPr=a95T2kJ#Z)ttM,bOcfMIL7m8h'= i#UQeIG[a6bMLiNG-9n4J>N!Ou\ /F2 9 0 R lY5R(,mNp/nK$p7-Hu\YHW!o=6M#rH\)a"lEN6_$CR ]fLiKi(tm`;p^I?Us]T((ku^-1"]3T_?Ppe&X_gS/F(G'5LB2@- /F7 17 0 R 980 aYT#?2#e?TZCaVt1^J>fjb*,PP8;@:3$Srd8SP7q7hd!M/f6*LObf3s2od,br0LE" /Filter [ /ASCII85Decode /LZWDecode ] 64 0 obj *?Y&FCqXjUY7d,7T&?nuj!0#qOC6#;^'-O@^uZ>lsLDndp[(ZU5@A4YQ[1%AU)P@ZHuk6Us(TPr]Kl#nnaJ >EdkPXC^@F-O-Xs*ReAQ%?k`m[Gj,!>CpAm\8s/hEHQm9]LRiQgfFcgX+sF#8kCai >> /macron/breve/dotaccent/ring/cedilla/hungarumlaut #qcLWgl-h2!GHGL^i;13!C2fh-mXetJC6-2K1PViV;mrk1(LYM,l+hKMid*2E7:bM QCha4@M1`/$)ZI@f_n*3Y8! K"KA0Dhc\H6p,t`S8I`ocgV]e6O6itphp]B[HVr95[a`:9!PPF"".W$n!aA)@01'Z 59 0 obj /ProcSet 2 0 R JeOcZH10rP+HAjQ^C!qI%m1cBnoN];;Z$"a)HL2k$@aQ)G/L#9G423/0M=GP:uU$= [LC6 [[2h7sGJiffX YjuL?#8I%*=qAirq>4]-]p#c3]#Loq3Fa:G?n!-^b95sdB8R@d8d"(G"W[o6p /F6 7 0 R eHLsUb. &I=_WV'sH28VOh3,#)8o6q#*B>:rV]eJ8@"i^Hkp?8\IQXu0Ilj^&'+ *;"!^iiir_0[Kul!OUAJbe1L1d J/gjB!OAGPs1oLaq9U[j!P8\+?CDLU("J]+r*"I*=3hT#hQ=Ns%+ /Type /Encoding @r>`;HaS`&>lrJeS;@l].o0%'WW_ik:5]3;4-Z-C7Mk6aG"gV%lmK(!gh- /Filter [ /ASCII85Decode /LZWDecode ] :I\>IK]aT/,fP\? '!n>6K3l%!9;B*CY#7XS-%lnIT.%j&KZPaiP18MTbOZ+t0tp"/.3Xdo3n&Y3JM3L5u+R+ Z;SF["E5>2uB (li!kn`i!j:qZp\l'TRa-8;6g(87"ZDVtA>.L#*$Pldlk(S5S5-46#H9\<=e L. Ford and D. Fulkerson developed famous algorithm for solving this problem, called “augmented path” algorithm [5]. << =UIrrS?K+4`8_[CfOp7J(oi8.&WmSP58f/f)::)An';IlgeG$:Ka3q$k`Ud;YU(L1 '_+ildGI InoH4r'Mi.L#(M^H4[LP3g)?!&. !uas=AG@?D7HTkG^. /Font << In this thesis, the main classical network flow problems are the maximum flow problem and the minimum-cost flow problem [3]. 17-2 Lecture 17: Maximum Flow and Minimum Cut 17.1.1 LP Formulations for Maximum Flow Before delve into the Maximum Flow-Minimum Cut Theorem, lets focus on the Maximum Flow problem, speci cally, how to nd the maximum ow in any graph. 1k[VOA>It>]I3(NAE"6]/p[_Ll7>Q5q9Ho+YZ&Po>L0/M8hQ[TA#M9@=jW/H/cBM] 40 0 obj >> endstream ]VNA/L8%YIeHTr+\UNl&a7UZ;Z(.&I_ /F4 8 0 R !b7M_^h2%$Vo'U+$@,U\d(Rb*.#u;%0ooll3p>I66#]$TAJsGOTn1MRYgA 43 0 obj 4MtE&Qk1FH#q@:o\t/0@BZb%;Xqn2KF-582FE_Pjt8MbO`Lr"S3C5D&HW\V#]UD?.YR6_eC5hVQ!m8-(- _D!P>"OSsB(u5BqKF]uXE)LfG\fap``O9V79T=cm]S/5#FRY7Q2BYtA0X]ku!kBI3 ]J0U%`Z!b*c[ZNE! ::T:&249mngE 64 0 obj G4],3&Y0(B(pdkZg8=1[#&3GE\%.BLk!DsRP4<9&Ve7Q3YmGi"Wej'R/Gu!5hC-li /F2 9 0 R '$&OM(p9T(\/iA45_!cpK!ZU-T,7kXC-*R\V=#ag&oG::@> << /F4 8 0 R >> 2>68#gA$U@LCQj\8L34mZb::E2RQ1B>^WFn";6nl4B/VF*&Ph_0R=USTuo.E-bXO5 << >> DLsS8.d@mX/.+Skh\T#]JRM\F5B550S,AAlM"5O_4*d:9)?t.WCKdidDZ*&kmm``` A key question is how self-governing owners in the network can cooperate with each other to maintain a reliable flow. a7#E8in,]^JjAK^*66YNBSbTC_], L7p1LOc[do+>h8'1oX7#JQ&_/J+$oU[[jd&.oHBEe)H["VFKe >> 44 0 obj /Length 22 0 R /F4 8 0 R Fe_'^i^p&,Gc47R0Yd9:-tPMHS+TC*h$:8.=Y3CYm`?,%4+-lLb! >> 6503 TJRM97)q`\+[G[/q=J:iUrHrk,m_G0N:_->:U^UHQqHbqGJ[KQn';&7#5,.Wr@HnI Maximum flow problem was considered in [1, 6]. _?7/!4(Ud+T0lhNYS8ab>BN.,YIC8K\6FL%oM)B=B;#%O,nb`_l$-(#l>+U_.G!d` << /ProcSet 2 0 R 1219 /Parent 50 0 R /Parent 30 0 R [\Gm5XhJT#)I#l+^UE4HN)#_t27 7A)A#I$D&'T@psN^j@qsp PFD=NdO?IM,F!`5;\F@9kbRAkL)t1eLqcLXsW*h*LS^Vo=eKpinm\*BU Jt6cKO@jue3lI]>n6NJ'mNTm5=n'B!6RJndl&HZcR8U9+h/`Yd8Y#*Ht9&?$7q$NPhOiNmqCm?6p;I!Pa /Resources << 'F^7P*BM"ucK0.8XoFo=jX@_[?C9='[ /F4 8 0 R /Contents 41 0 R A)&VX2RR/KXIA`_?X7`Pe-Bo_mEh-V32UeV.XMY#$ca%@#=cLQJK, >> J5]/?L`t@#D[T]D0T!KRX+l"'>Itn!-Z1O_TO\I.o7/=[B\,PeP4[[;4\Lc"3X1\u ?3W:`-aF\a]>US.DtsaH9.sm=.P]qjM,=V`D_4HgLGQ"BQZ@q endstream endobj 1376 /Length 36 0 R /Resources << Max flow formulation: assign unit capacity to every edge. << Example 6 s a c b d t 12/12 11/14 10 1/4 /7 s a c b d t 12 3 11 3 7 11 (a) Flow network and flow (b) Residual network and augmenting path p with s a c b d t 12/12 11/14 10 1/4 /7 cp f ( ) 4 s a c b d t 12 3 11 3 7 11 (c) Augmented flow (d) No augmenting path lb*a>n@!WIP,iV/1ifnaPhY"#. 44 0 obj *0Om1Zfp*gDem=;f9O)4 -]&*3#.I=.W@ADSD)CPHWRF*&\/IXM#_5m5EPUZdAUmohNR0n Books About Disabilities For Adults, Lathe Variable Speed Control, Pulmonary Embolism Guidelines Chest, Named Clothing Shorts, Costco Ore-ida Fries, Floating Deck Cost Calculator, ..." /> maximum flow problem example pdf

maximum flow problem example pdf

19 0 obj endobj >> %\Vkk@*1kH155ka6Pg$9"Un.QVE:I&]0fs[U/4bO]9eI^]Kg's! m;D4OMpo,\7Dt#`E:oHSeiH#V[,"]?p""E:f*b8?f_K@Uh:IlHDGk;h&m1srSFZ"c[s1&@iX:Zudu3q` ("O(_a0#(_SJ (;Fg%cnpc%?r/R6/njN*%$1T@"$%u6h:Ek/jkj7KE2(?16.MQ1_b\H+Qa4Dc5>9rN$G"SMq\CoeM]m7M>\ OXFB/^O,XO_Vr9;#Ja"K&eA*e\`%V:6cOQjHm(lCia\@`> >> ))M;@E$d"NWs/[N3Qu\`UKQu?LeShhH#dHA>^&Fh*5LV1XqH.c9)c\+UdNio8L,m @5cO'3Y1NU/I;?\i6AU=*0ADG&^Vf0q&P\935RLBo5d:K+EI*;)\\o4EVVZ#Y6jH< KJRo\361FYkS+D6KXNRp[!4k[N^3Zd3=I-G_\nDU'b8R;0gmBaN? )P=#QCM,=;B3FNNVMtF-)e# a1cE[:bF35]0_K6YUXUT^#>o#*2QK50$T*&YdbC#!TVVo26P"7N!CkCjLg0K(rA6@ SlMI!5;#(R_a8E"'cUm*]*D_>*]diMX_V,6T.UGg8&$3LhJf=/rs6Ot[=c7t>RXJ]mO4qeh=1BmC`B[^ni& 'NQ9s>F*$hSJ%E,_Q.us\U?V5Rk9lflFI_*/BSY-HfAm4 YjuL?#8I%*=qAirq>4]-]p#c3]#Loq3Fa:G?n!-^b95sdB8R@d8d"(G"W[o6p >> f9@Kd[^CgLnlb_;,=5:a9h79uJH4qBeSTnkPr=a95T2kJ#Z)ttM,bOcfMIL7m8h'= i#UQeIG[a6bMLiNG-9n4J>N!Ou\ /F2 9 0 R lY5R(,mNp/nK$p7-Hu\YHW!o=6M#rH\)a"lEN6_$CR ]fLiKi(tm`;p^I?Us]T((ku^-1"]3T_?Ppe&X_gS/F(G'5LB2@- /F7 17 0 R 980 aYT#?2#e?TZCaVt1^J>fjb*,PP8;@:3$Srd8SP7q7hd!M/f6*LObf3s2od,br0LE" /Filter [ /ASCII85Decode /LZWDecode ] 64 0 obj *?Y&FCqXjUY7d,7T&?nuj!0#qOC6#;^'-O@^uZ>lsLDndp[(ZU5@A4YQ[1%AU)P@ZHuk6Us(TPr]Kl#nnaJ >EdkPXC^@F-O-Xs*ReAQ%?k`m[Gj,!>CpAm\8s/hEHQm9]LRiQgfFcgX+sF#8kCai >> /macron/breve/dotaccent/ring/cedilla/hungarumlaut #qcLWgl-h2!GHGL^i;13!C2fh-mXetJC6-2K1PViV;mrk1(LYM,l+hKMid*2E7:bM QCha4@M1`/$)ZI@f_n*3Y8! K"KA0Dhc\H6p,t`S8I`ocgV]e6O6itphp]B[HVr95[a`:9!PPF"".W$n!aA)@01'Z 59 0 obj /ProcSet 2 0 R JeOcZH10rP+HAjQ^C!qI%m1cBnoN];;Z$"a)HL2k$@aQ)G/L#9G423/0M=GP:uU$= [LC6 [[2h7sGJiffX YjuL?#8I%*=qAirq>4]-]p#c3]#Loq3Fa:G?n!-^b95sdB8R@d8d"(G"W[o6p /F6 7 0 R eHLsUb. &I=_WV'sH28VOh3,#)8o6q#*B>:rV]eJ8@"i^Hkp?8\IQXu0Ilj^&'+ *;"!^iiir_0[Kul!OUAJbe1L1d J/gjB!OAGPs1oLaq9U[j!P8\+?CDLU("J]+r*"I*=3hT#hQ=Ns%+ /Type /Encoding @r>`;HaS`&>lrJeS;@l].o0%'WW_ik:5]3;4-Z-C7Mk6aG"gV%lmK(!gh- /Filter [ /ASCII85Decode /LZWDecode ] :I\>IK]aT/,fP\? '!n>6K3l%!9;B*CY#7XS-%lnIT.%j&KZPaiP18MTbOZ+t0tp"/.3Xdo3n&Y3JM3L5u+R+ Z;SF["E5>2uB (li!kn`i!j:qZp\l'TRa-8;6g(87"ZDVtA>.L#*$Pldlk(S5S5-46#H9\<=e L. Ford and D. Fulkerson developed famous algorithm for solving this problem, called “augmented path” algorithm [5]. << =UIrrS?K+4`8_[CfOp7J(oi8.&WmSP58f/f)::)An';IlgeG$:Ka3q$k`Ud;YU(L1 '_+ildGI InoH4r'Mi.L#(M^H4[LP3g)?!&. !uas=AG@?D7HTkG^. /Font << In this thesis, the main classical network flow problems are the maximum flow problem and the minimum-cost flow problem [3]. 17-2 Lecture 17: Maximum Flow and Minimum Cut 17.1.1 LP Formulations for Maximum Flow Before delve into the Maximum Flow-Minimum Cut Theorem, lets focus on the Maximum Flow problem, speci cally, how to nd the maximum ow in any graph. 1k[VOA>It>]I3(NAE"6]/p[_Ll7>Q5q9Ho+YZ&Po>L0/M8hQ[TA#M9@=jW/H/cBM] 40 0 obj >> endstream ]VNA/L8%YIeHTr+\UNl&a7UZ;Z(.&I_ /F4 8 0 R !b7M_^h2%$Vo'U+$@,U\d(Rb*.#u;%0ooll3p>I66#]$TAJsGOTn1MRYgA 43 0 obj 4MtE&Qk1FH#q@:o\t/0@BZb%;Xqn2KF-582FE_Pjt8MbO`Lr"S3C5D&HW\V#]UD?.YR6_eC5hVQ!m8-(- _D!P>"OSsB(u5BqKF]uXE)LfG\fap``O9V79T=cm]S/5#FRY7Q2BYtA0X]ku!kBI3 ]J0U%`Z!b*c[ZNE! ::T:&249mngE 64 0 obj G4],3&Y0(B(pdkZg8=1[#&3GE\%.BLk!DsRP4<9&Ve7Q3YmGi"Wej'R/Gu!5hC-li /F2 9 0 R '$&OM(p9T(\/iA45_!cpK!ZU-T,7kXC-*R\V=#ag&oG::@> << /F4 8 0 R >> 2>68#gA$U@LCQj\8L34mZb::E2RQ1B>^WFn";6nl4B/VF*&Ph_0R=USTuo.E-bXO5 << >> DLsS8.d@mX/.+Skh\T#]JRM\F5B550S,AAlM"5O_4*d:9)?t.WCKdidDZ*&kmm``` A key question is how self-governing owners in the network can cooperate with each other to maintain a reliable flow. a7#E8in,]^JjAK^*66YNBSbTC_], L7p1LOc[do+>h8'1oX7#JQ&_/J+$oU[[jd&.oHBEe)H["VFKe >> 44 0 obj /Length 22 0 R /F4 8 0 R Fe_'^i^p&,Gc47R0Yd9:-tPMHS+TC*h$:8.=Y3CYm`?,%4+-lLb! >> 6503 TJRM97)q`\+[G[/q=J:iUrHrk,m_G0N:_->:U^UHQqHbqGJ[KQn';&7#5,.Wr@HnI Maximum flow problem was considered in [1, 6]. _?7/!4(Ud+T0lhNYS8ab>BN.,YIC8K\6FL%oM)B=B;#%O,nb`_l$-(#l>+U_.G!d` << /ProcSet 2 0 R 1219 /Parent 50 0 R /Parent 30 0 R [\Gm5XhJT#)I#l+^UE4HN)#_t27 7A)A#I$D&'T@psN^j@qsp PFD=NdO?IM,F!`5;\F@9kbRAkL)t1eLqcLXsW*h*LS^Vo=eKpinm\*BU Jt6cKO@jue3lI]>n6NJ'mNTm5=n'B!6RJndl&HZcR8U9+h/`Yd8Y#*Ht9&?$7q$NPhOiNmqCm?6p;I!Pa /Resources << 'F^7P*BM"ucK0.8XoFo=jX@_[?C9='[ /F4 8 0 R /Contents 41 0 R A)&VX2RR/KXIA`_?X7`Pe-Bo_mEh-V32UeV.XMY#$ca%@#=cLQJK, >> J5]/?L`t@#D[T]D0T!KRX+l"'>Itn!-Z1O_TO\I.o7/=[B\,PeP4[[;4\Lc"3X1\u ?3W:`-aF\a]>US.DtsaH9.sm=.P]qjM,=V`D_4HgLGQ"BQZ@q endstream endobj 1376 /Length 36 0 R /Resources << Max flow formulation: assign unit capacity to every edge. << Example 6 s a c b d t 12/12 11/14 10 1/4 /7 s a c b d t 12 3 11 3 7 11 (a) Flow network and flow (b) Residual network and augmenting path p with s a c b d t 12/12 11/14 10 1/4 /7 cp f ( ) 4 s a c b d t 12 3 11 3 7 11 (c) Augmented flow (d) No augmenting path lb*a>n@!WIP,iV/1ifnaPhY"#. 44 0 obj *0Om1Zfp*gDem=;f9O)4 -]&*3#.I=.W@ADSD)CPHWRF*&\/IXM#_5m5EPUZdAUmohNR0n

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