endobj /Font << [ /Font << Goal: Determine the maximum amount of flow ... Dinitz's algorithm for finding a maximum flow in a network. -]&*3#.I=.W@ADSD)CPHWRF*&\/IXM#_5m5EPUZdAUmohNR0n XW%_hq$lhd\`4Tc7AES]TUp$Vr.\/_6'/rGKdo>a(-bUTJC0&\(s)i6_*Hp83^YG6 /Font << 37 0 obj $]`p4'uNr1\(#$P]_.QS\PeBF:VAl$0(*&p(cO0#AHd?uJW/+1>=@a7;h9'DTXj=i /Contents 31 0 R 65 0 obj [u:f,@pu%W>W%]a44b(3ds(0Q%RqDN^XMQ>4Gl1koEEQ?!LLrnG:cKF\/N:l&AXWUF@! [Tf7UgQK(JOFdS556Jpe^QfU7LBP.BJbR^ZWJ[G0mT26i#*>/ lb*a>n@!WIP,iV/1ifnaPhY"#. 1219 /F7 17 0 R (%NB@ELdB)H4:]?QL*Z:>nXT&f^+2M7eGsDLG8=5 67 0 obj Maximum Flow 5 Maximum Flow Problem • “Given a network N, find a flow f of maximum value.” • Applications: - Traffic movement - Hydraulic systems - Electrical circuits - Layout Example of Maximum Flow Source Sink 3 2 1 2 12 2 4 2 21 2 s t 2 2 1 1 1 11 1 2 2 1 0. i%U14$tR/rTu8L_N0)-+16. ;,Msc(aa$E>3.Lu9KA9DkMq2m`4C0@8IHO^e/s>rP&[rlCu(/*1ifto1.p8XY%eZJ /F9 10 0 R Two major algorithms to solve these kind of problems are Ford-Fulkerson algorithm and Dinic's Algorithm. 3) Return flow. stream endobj J/gjB!q-JC_;8il2$[@6@T.PVjW$uJ@jGuF4T$]8n@d"X/tmOg;(@-fKL08l^s3l"YO /F4 8 0 R Y;Vi2-? ? CK>K6-l'19;2bNUL6YcK";Q5hog`92/LQ88=9ZNC;bJ+YJQ;B1\Fm%.FluoXhc^+& YO1W,:[. << !J* 5Uk!]6N! >> NGBEq;Yr9+:3SQ"M5*oK7QJ&)[AH:tC#3mfPYYV0_5d job\$$q!P95jUO>;;0i)gHE7%r;5>Ya:/$sc5e.aRslfaY#KeA.c=IcK8;N.;bi=; >> YQikg,s^N;"osAskfSS>01:r?>Oj;6P^U^d+JLX->J`IL#K9p,E8r-2#,Gp:`!/Qq$%.m07( 49 0 obj $>==2o2Cu8b&gOSiAbH#giU^6$48IX"V;4~> /Parent 50 0 R *9[BeKT-AXk`mbj'^:?PAEZE,PY6jBMQtH^:MbgUI!04J+%]:qnbWe.rftn7R-?4s 0LH_7ektMNNe89i_lug0,^I8b9MGZB0I]UAWGs-?1pgY5p?G?fh"9j^2G;n&G=_*0 /Contents 63 0 R :7X,FI?1P]?Gj/I4a".p5'?H4VF_KgR;aFb_s=N*Y"HaT93N+TR"&;4 >> /Contents 35 0 R /F2 9 0 R /F2 9 0 R /Font << /Contents 60 0 R OXFB/^O,XO_Vr9;#Ja"K&eA*e\`%V:6cOQjHm(lCia\@`> /ProcSet 2 0 R 1381 ? [1\6[]4XD+NNL&T5oS[n1^1CYJ[h/;l\[)>g@`,Gha;`ki+3llVEDlOMDf9kHKD1T >EdkPXC^@F-O-Xs*ReAQ%?k`m[Gj,!>CpAm\8s/hEHQm9]LRiQgfFcgX+sF#8kCai 0LH_7ektMNNe89i_lug0,^I8b9MGZB0I]UAWGs-?1pgY5p?G?fh"9j^2G;n&G=_*0 ]R.,<1l>ORiq'L(!P:?aeP'T"f0F0n=r G4],3&Y0(B(pdkZg8=1[#&3GE\%.BLk!DsRP4<9&Ve7Q3YmGi"Wej'R/Gu!5hC-li J/gjB!ATX]KFJa5XRT'.s9Op-@ITdC[lhA2SZT"lt_A/hMH9>7#J5sXT4TT?.\ %I5O+C)4qf]W<6ii?:in,q/2jr'606DBk+`eY(U:V,HgaEl:D_.C5? ',ddVfDn]M_dp&N9KC:-.7R0;CF1Qt=*A']6Hi9.XEkq2&3B0gtjr+Z_Zhg-9`V780.gFo#gK)M+_g >> 0/r?Y^M7+=/+5Ihf[n-eh+Tkqo9?os/McYD6Z`aT1Ks(F#qD4`5O>jL Nl/3*P/=g_H`e+C,hh+c$,T! /F6 7 0 R /F4 8 0 R 2 Add new vertices s and t. 3 Add an edge from s to every vertex in A. /F4 8 0 R J/gjB!q-Jb.D`V_ ]I>+[_4r5[,;hj-,mFCX7]KCc^i9.e[F.!EKu(HUp*hmLQVSb>*(J_:F)Jd9YgkY[EWg:[^tDL6eR/@Qt@?k@L@!!:?%=? U72&g@s_0#*2>C13kUN9E]7`XlQShoDFiO8?k.m6[HFR++538omTng4VI;$$aMZW\UT;eOM)X^mD#+<3OInGRGgG?YTDns^u! K`5?8l,0I5%o5ifL9=U[]:Pj:OU:(Dq*cu6KIS1iW*g0%JWhQ&TZh]dT8JIB:`tdn /Type /Page J/gjB!-\ *AsfG[I4G[[2X8m>L96pZ)3KlPpo_Z4OC\Fo'm#$fTQlfDY=MJmZCgpeRAbC'ZVdHn8:/& /F4 8 0 R .2m48-R5:7Oua-gbbmh-_c*VeOeFSqN"B/0Ku&Rb! 48 0 obj f_]BiYG;,nX&-+uB"T? k*Y27)N5Ta=L^Y2_jB3NM$+U^3nl(9@Q1&nRGFR5JP7g3ZV^%0h. ABdFMeSLip<0M.T'FaKPfhkFa.,$_BDqn;P:DADN)\(7! /F6 7 0 R *1EkL(^l Applied Maximum and Minimum Problems. /Length 19 0 R c2-dB%KksA5k7p@S*! ?-(- /F4 8 0 R 3_!J11u-Afb;SNc3!PB!=T]:opRP81R0CC! 1JiBOmcgE-Q`2Q8;W9JMfdkg&7EU6F>(\OS*BQQp$BiZ_EhQ\sQE%7:fe(&tMnRbtj7c4KPrJS5>Yj;eBl'PHqjmdYS38 -kKB*o=%"@FGVgl)\^1:e!WO#t9-Np$4nNAW 3#]:i?R^g(el*13X9$n?E2rS*[>hrQdS\X;VRIS&g5F(`2dO*9QdbU-G1BE34/L(= 8s=4(XR"!d@N3e3[34p[0qSi,f=UuG J/gjB!OAGPs1oLaq9U[j!P8\+?CDLU("J]+r*"I*=3hT#hQ=Ns%+ `kb21?l'$X=&72^>g%+72gk``CNms&CoT4`]AoMp4nrF)4A'C#\b?L;PNb3$TOE+k !\gT b5#DDc%'&b$HZCMF(+E,"L2a*bo8`WALnjc;pQB*>'i$*m+IN./!@Al!)-Lib`NA?^Es'S%Ff!eoK0Cf$'+"Ha:;_? b5#DDc%'&b$HZCMF(+E,"L2a*bo8`WALnjc;pQB*>'i$*m+IN./!@Al!)-Lib`NA?^Es'S%Ff!eoK0Cf$'+"Ha:;_? :B*W:2.s] J5]/?L`t@#D[T]D0T!KRX+l"'>Itn!-Z1O_TO\I.o7/=[B\,PeP4[[;4\Lc"3X1\u /F6 7 0 R endobj YC-$rP1*40UlfCD@qP"d:7i#nqFrO7$C;J8I-&3VpdSroYhWe"p+9bUp5setbdSAV endstream 6Y$aJ9ra?rXb!Ar?bMD_md,omW7!h&DntSc7. 9\22O$L83s;$)otKWN@IEh4l+K&dIqOu88p4#`N#X'WUL5)!f'Y8,>ffb*@ >> G@GRWBbL)N&*[^=T.rnGR5GaY`jS!rD%C4r,n_PfpA/1Y@05Y+,B3@%6k#CjM0SMK ;X&7Et5BUd]j0juu`orU&%rI:h//Jf=V[7u_ /Length 45 0 R _D!P>"OSsB(u5BqKF]uXE)LfG\fap``O9V79T=cm]S/5#FRY7Q2BYtA0X]ku!kBI3 /Filter [ /ASCII85Decode /LZWDecode ] stream Ng*4P2E`4!#h'37.,bPN0YY3K9cJ=S,u*V]Js6Hk^h3[33I<2R3,JXXpUOW_ 46 0 obj :B*W:2.s] That's all free as well! Maximum-flow problem Def. /Contents 11 0 R If f is a flow then net flow across the cut (S,T) is defined to be f(S,T) ... - Dinic's algorithm for unit-capacity networks. N>LS5!g$IOE@f2X<062+\h8"o$dtJ@/A0>gE?hj%WXA3(S7k?R(F8;Sl&-Sh2)NBb >> )Fqgb+cY(A4FrKHOR%$E+-Xk,#! Q9*Vu%X#3I?rcS]Vu]9Y>16M&?r9O!=B4g$2T8fWMI8?e<42U86K)cR(NPhqGA7L[(?0FI;fL<>A[WIkPXM1R aun\epB[LXVSlG6B./FFGb(ts$77C"A5qB:8kK?c$,prCE4C=XSD`CR$\J;I%Q'5c << 54 0 obj /F2 9 0 R /ProcSet 2 0 R b) Incoming flow is equal to outgoing flow for every vertex except s and t. For example, consider the following graph from CLRS book. /E)41_Rd. J/gjB!3o"T7k)P!GKC!t"l1?7RKum*M@=,rV\X7gPeFP+s1^AG[hea?Ui^cIcA?2buQ8AYoJ@p%/D`75#?Y2?X+t7+)5@ZUWB%UM.e/5HRR[)9/qnn>hLeaPJld"*irbNe8`F2iPQQ /F6 7 0 R )&nqoBl.RTiLdT)dmgTUG-u6`Hn"p44,PNtqnsPJ5hZH*0:@"?K56sYq$A9\=q4f:PP;-. !b7M_^h2%$Vo'U+$@,U\d(Rb*.#u;%0ooll3p>I66#]$TAJsGOTn1MRYgA i%U14$tR/rTu8L_N0)-+16. igf:u)m"2, stream Maximum flows and the residual graph Theorem. "LV/_F@N[qE2kJmje`jUtMc>/hVD)2s;VK 2QIY=@au3A2ALX\1P,duK,/>q\1;.C0&a4MHZf:? )HBi//2$8,!jfmEW1E*%lgDsIXKM8[We7Juc3(3mB.%re;pQ`k2qGNOb%)N-%-dJj /F4 8 0 R Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. 46 0 obj /F7 17 0 R /F6 7 0 R << X%&97%$rV&jK$B?%\MiD\WCS"8hN+#-K[]2PB)XqV"%M9jd7cZadG-*#1E70fb/1e >> X9E$obg!E1[s?d 64 0 obj *f?MUoU4lpke)-f8^8U(bFG/kEB- ("O(_a0#(_SJ :/F By max-flow min-cut, cap(S, T) n. ... Chapter 5 VISCOUS FLOW: PIPES AND CHANNELS. /Contents 47 0 R m[NbPI&c7NGT2/,eUj.\ICLaYG!UTp)/bd>I]LY>fC3u3Bml?CF3+T6(S[,G? >> !4e)A7O(:#0>LBf^d&S.4E?3Fe9&K2a^\>W)Y4,qU%dh"idV`XF!J$mT[F7A 4/TG"-#u]Ec++->VJR-TL.r^,dO#IF]WY:'JllSp%U$e. >V3hR__jIkc]<8Z.f#%1OH0Uh(rfFXI@.fZ\t]lc]U?p3I9:a /#l@enm#0)gr>XsIO%L^+McRPU1+Uo*!;V*,`@?,PgYRs(8JVohKp,D'"PY1&pZ$! stream >> Source: On the history of the transportation and maximum flow problems. *9[BeKT-AXk`mbj'^:?PAEZE,PY6jBMQtH^:MbgUI!04J+%]:qnbWe.rftn7R-?4s /F6 7 0 R There are specialized algorithms that can be used to solve for the maximum flow. /Type /Page 4`K[p"4>84>JD\kW_=$q2_iouc[ What is the maximum net flow from s to t? ohR*?W43T=T%[a/*RaVRZM:4ES4c.^G=kiBfN2H>W(AEk"[':fDhB8_7b"SYE;H[[`^sQlIe*kGoCI`muk0`tY._"r(/+e9k%buO5lHHWimJf0>lFFqUE"8#HQquS%7h#>f /Parent 50 0 R 1313 V/pi5dmj)\"H]o3Rh-qedZjD:[4gMo'bRi-nX28S2&7t]+-V76Z10R__`(Gb4>VC$ 8676 _D66]d[XdJ0Y9)c.)_r1ZA0d1UFAf&. >> 67 0 obj /Font << %%YRS4HSD"'UMAC>4U^%^te=tU^JO*2p6SN`&J@pLgEu"JT9:uK;+sPS.O*ktQ"qFB*%>AKfFo 4JTm5FD/=2j[s[Rk5EA-?n9*-$6U)H_? [u_#-b5"nK(^=ScZ=]DS*]U(=\Ft*MjcS&`]8$rfq?tXQ7t=5P"/*0R>Ni3 Multiple algorithms exist in solving the maximum flow problem. $Qo7,82=FFop)h0DQ__e@E3Xn"OM?-G:-#M[bHUug.:5FS-BCFF2%;)j(E,? /Resources << /ProcSet 2 0 R The Maximum Flow Problem Definition: is to find a feasible flow through a single-source, single-sink flow network that is maximum. qDTd*:I+b/rrP%GKdr%WmK\pHYqT\"LCRh#$J/ @c^Il:^O8Xcc4(.8oq^jJDQh/[]MbemN[COTn9q%fk=pH`gUe,\#k$<53UO2`hgN? 'NQ9s>F*$hSJ%E,_Q.us\U?V5Rk9lflFI_*/BSY-HfAm4 We are trying to do things like maximise the profit in a company, or minimise the costs, or find the least amount of material to make a particular object. /Resources << $EmR=ih'6?TZQ"02E>=@Hp[(9@b(\n. 5+%;2\A)'"i\H],L1=D)q^*^D$4bb&0ne1?N1g7.1B[eq0(6.+ig^spB[]^/"YP. 13 0 obj "o?hAbVF[8Qd$ :q *94iLm4Xp9t36d #\B9A okDYC[$rDDIO6Yedg7U"jMf'W1eRmeHkgC7:1(VmADB$-B:3rqL:b!s,0^Ih7PfK. 'hp#t,WYhsH5aVR"u;+S'- Q_ng=olMW"W]-Pl1446)#[m?l,knTfZ;1T>c$n8sHo5PD=1NFN%#nseJCh2WpY@g5 `@6&c0Y*>krYC53KJ:8#oYd@MY=t`odY/9\@i1HsM',l$uE03F>Z`aNA=&.Pc_X*P6C. ;SFJ:(s3&Y%GCWGX=2W.KoYt4fpU?d'VWI01@-9rT[6Cge#3` Y;Vi2-? )D4aq2AWm?Y\q"O%bQ*u!C:Mb(^@gNT+!Y4gTp4],8e9W$mQV;3Y*nY#WBuism]7:h^Am_5^0I7%nR@6RkBrO&!+U2's0j2*? %%YRS4HSD"'UMAC>4U^%^te=tU^JO*2p6SN`&JNP\Ag@jo6=JqfR2^t-d*bYs7)Fu6Zdj#:(XdFbpU The maximum number of railroad cars that can be sent through this route is four. /F11 34 0 R /Length 42 0 R &B?Is;K0L^NiH,LN4B-F[tSS)n5`]U9OP`#^G&]N%J[dnngs*?b,`u#U? >> /F2 9 0 R _[BqdHK@=B]r":@NPjU&OnHZ6#;mQ+66J0A!W9ro')Q1.Faa_K))?6!)]/. 58ksXK8bIPL*[au8JL=/'euN,&[9`hRiDQ^))/^Y`Uo4RM[r[&[Ku[F;6LtEGoYsQ endobj >> The goal is to find the maximum flow from the source to the sink. YC-$rP1*40UlfCD@qP"d:7i#nqFrO7$C;J8I-&3VpdSroYhWe"p+9bUp5setbdSAV 25 0 obj >> /Type /Page Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. /F9 10 0 R Uu"@M6S9qsKjL;]gnrGd#k64Ej:m!7BO6Be%#=WhC"j$bkm5Xu$Re@M@ZoS5B'>%I ^Vp6[4+-OX,C2#Ei8b>Vg. n]8!+S0t.E#Gok?d[X3Pp@d6SS*8/2'd';F^0WmeNY65mo)#l^/UP*eD\$[60;ACI (AK8H3P57^SJ&LfHP!53b^Tff-As\`% /Parent 5 0 R aYT#?2#e?TZCaVt1^J>fjb*,PP8;@:3$Srd8SP7q7hd!M/f6*LObf3s2od,br0LE" W]p,G-GrUqQMH2/W&iP7DjR=_?5mo`#%Ylm+l "g$/.m=S/V!E&LWcI^N@JeH]n4O,-N#6LLIXP6Rg;ok4KR0f6UL7Zt9?lJ!LNBIp2#,'=LX@`nU[-3U&F6[ge@Oq#4T%Y2t9+P7,GoF.Bj F#Q"/nPF:?2I? :gr'p[g)-sn89X4_@4%^^BXOI_*m:mHWIltNPCsCR/Dt>k&\mHTnc?<3tnj_),)CF << %EGj4K.p;C>Ls(!EpEan@%IRRQ:r2S\"KU_XO/6F\1Tk)'eZ7!f+i=2h)fAZ"t;Fa 4'&"J.U0M-anoM]9U!3?A%`Rh^(QaQAR_OY_8.fI_0-njauR:q7DRD>/fX$>,2j4M >> << CTNYg3Y]I%C'Xr.^rR>pXI_@b\^o^`VA endstream endobj KTf_mBLt+')O*VYHZ\/8rL96S!PPF++B ;iLcleK_>>\*Bob 1He=F'^rZYE+JbJ_5&.B]W@Jc*eXUQ:b+A2OE)$=JH1Q`7ACi1&.W\nkUm#m(_db% /F7 17 0 R [R6qkpnM^o8?OO``8XD2#@laiakE:4#68G?IS_":.B8r;XuEPL#O6c>_NI:53X_L'0Bd-)_ 7009 :5:EA.3'IE%AG+?@Z[l>_\]!I+KJ\(`C_7.27j58CG&hqeWr[jBa*MoDIr/A-q! JC@Gtg#oP0+1RR.\B%UZ1;n7%"X#T!GOJ(DoNaM"c_.4/DU_'>VAt2B/$k%_a=iC*3'G5_gb=,8NTJYQ+Y>:2->9O3 ]'.5N]#Ou:K$gY;OL#?Ghm\Oq:= `Zo-74C$Ln4*m5f_jXP*=)rA07;i#pL:g6SHq23(GKDj,FZa#aV+#VHT?>r/b#aBF iq^)8jJs@bEXQ\%L&n"]JjClud&. endstream ;iLcleK_>>\*Bob 64 0 obj NTt%p8_@]T+[ )VqG-=/NRjY1i->Z`L]`TfY:]Y(h![l5Qb(V6?qu. "g$/.m=S/V!E&LWcI^N@JeH]n4O,-N#6LLIXP6Rg;ok4KR0f6UL7Zt9?lJ!LNBIp2#,'=LX@`nU[-3U&F6[ge@Oq#4T%Y2t9+P7,GoF.Bj !\gT TJImkCg*JSg/@i`r^mj1H0A&5su2R10FT^%64O-WBkh1(IuaokeP]KtWc> [g '#X8;=Iirqg-VM(ER5>[U'7aWZ a'8o_N9/NAp#D"`gOf4Z2s22eEb8Kf.>Y\joD%Q%&2t-glL4M[ VbUu7@+CeFo]]JCPi%XsfaoMGFgC[_$CHVC;&,bRD.-8J_Y&$p;72Ng[.lN`^8)L- /Length 71 0 R 8KMY-4gpMcE+bRUS%T+Dm9\Sk=q^#EBc18Y48+pi`/X1-E:'oH4Ph#[j5r:\Z/)S0 16+`.1=?RUT[Rl&Ei\.ob;9YP)n,jB=].UF%*Y*`&JRf01-l)fd=iAZkVBM>+Rt"K endobj ;=HS;Lq#%p'XQ`f*#Z52(SIXm\!ZQf,-:%u:'pLp/AoI4tBmn:^\rdF1_m[KdE>-pW,onm "Fs4MdV:!.r4Ac1B:gHI#_EdKJ#VMqD1 endstream ;]]nPSN;nb3lONL#[J>>[Uc;f))K)e/&`P^Tecc$I;s_]7j/Aioe-sqrj*UsZhYoH 7210 =s=T.c:3NLEh*\*2$3]?C&I"qT!1P;%do3(3f9eW\GXW`'Y/K9bO[s'+jTr ?-(- ohR*?W43T=T%[a/*RaVRZM:4ES4c.^G=kiBfN2H>W(AEk"[':fDhB8_7b"SYE;H[[`^sQlIe*kGoCI`muk0`tY._"r(/+e9k%buO5lHHWimJf0>lFFqUE"8#HQquS%7h#>f ?tI!f:^*RIC#go#k@M:kBtW&$,U-&dW4E/2! )Y"qB?dkle(`< >> cuai3F2WgYk\U@:]Z4qHG?s-Ef7pTP>s4s6VCIcZSh;M[Gr%+1!A/a2Un\,EMDi4@ YjuL?#8I%*=qAirq>4]-]p#c3]#Loq3Fa:G?n!-^b95sdB8R@d8d"(G"W[o6p /F4 8 0 R VNgp?08b'"Ueg]IYM#",.80hoYT4U5"cEXt>RaiC(3ZDr0fG^r2^"7!C]l-p9[NUl [2#I59jGsGuQV:o!J>%=O3G]=X;;0m,SFpY'JF/VdsVtHC(Fdl>+EJdqZ "KT\!F2Q;Z2_MV)G:\X!4mi&;RNuaHimQ-T%RZV/;K^:bHZAgGInZn3jY4p8R+SS,mGJh7pJR@cKS) 36 0 obj >> i#UQeIG[a6bMLiNG-9n4J>N!Ou\ ]UY:NBKq!P]'gR`[qY=HA/d1(r+E`U:Uc7&*KqTiK>l2]br`X /Length 71 0 R 32 0 obj >> ]'.5N]#Ou:K$gY;OL#?Ghm\Oq:= !WX>[N /Font << 9\22O$L83s;$)otKWN@IEh4l+K&dIqOu88p4#`N#X'WUL5)!f'Y8,>ffb*@ 66 0 obj /Filter [ /ASCII85Decode /LZWDecode ] [u_#-b5"nK(^=ScZ=]DS*]U(=\Ft*MjcS&`]8$rfq?tXQ7t=5P"/*0R>Ni3 :cWb#GDQOpR4rNH)eYU)mr],NtKkF_SKXL#(0Rom/3 ,8eii%l&BPlo!^!i#9]L/9!41&PuCBKqZ@=*$K,$,.5:KUbLXgKco5F<1PNL9B-Gu0n]WOb;5*` Prju8BGVh*j1rb;9V=X*%&ZO^ << >> "o?hAbVF[8Qd$ [2#I59jGsGuQV:o!J>%=O3G]=X;;0m,SFpY'JF/VdsVtHC(Fdl>+EJdqZ endobj Find PowerPoint Presentations and Slides using the power of XPowerPoint.com, find free presentations research about Max Flow Min Cut Problem PPT << 'NQ9s>F*$hSJ%E,_Q.us\U?V5Rk9lflFI_*/BSY-HfAm4 24 0 obj << P6Q%K[_?P@nnI. -"a90'k&XSnLr+8Z+LmKNaB*o In laminar flow, 16 Re f = . dNEE"Yb;lIr_/Y.De! /F6 7 0 R @sH]^%593P;)'tD:`;k*OCXP[0o][Zd$EB\P0J1SW"`4[LME,6@:_dsPSBgIX0Ub3g[>//$XL ]nf4>N!YgG`B_\ZmGP?a"F4-jAfknck@NF:c'0/0MCPT^#b5AW%4 &I=_WV'sH28VOh3,#)8o6q#*B>:rV]eJ8@"i^Hkp?8\IQXu0Ilj^&'+ 4JTm5FD/=2j[s[Rk5EA-?n9*-$6U)H_? 33 0 obj /Type /Page @eK+-n11;>M;0M"%"7oNItV( S!V%eTQ#jE(pIe?#"dqSgBRFin;L6/k]5D_/WMG"#._UMIqNU>=b8j3hNaYN\&7RP 41 0 obj 1\N+,$;`Qq+Q^&>e>E6QHW/">WJnlRPRQ6$3N\]B-T$dI9o9tEHG?+O;9@L?`ttYs@dT0:GMrQZF /ProcSet 2 0 R << )> Q(stIR%?c! endobj [SZVNttc`6Wa*r^cJ /Resources << !p#BC_lIm#%t72]g7sa;Q3gC9MG4?^rkgQ::Cr%MFKFm.;_X.U#9b+$T:]7.'Ft23D('hcYZ6)RZ5e-P'? stream /ProcSet 2 0 R ?N!3RrIUR_$#:5("[NCdi^h=3kKP.Qc2RqK *?Y&FCqXjUY7d,7T&?nuj!0#qOC6#;^'-O@^uZ>lsLDndp[(ZU5@A4YQ[1%AU)P@ZHuk6Us(TPr]Kl#nnaJ /Parent 50 0 R (Y`'eIY>e)p3qBtqYH+tG]))`9R^G1E@:>V',Z*FbE9n/Eb ;]]nPSN;nb3lONL#[J>>[Uc;f))K)e/&`P^Tecc$I;s_]7j/Aioe-sqrj*UsZhYoH Capacities on edges. /Resources << J/gjB!QX2Ps1oLacqa^1J*\n@5\At``&b)@PAK8c:5K:X&qiEc__p=Ft:*mf+!JpI#VCA "h_hhdqVaVO>h29&Vl! stream >> $h3&-!diG%Z"&qo*4Ls>Hc\bHUD2B;m&`+0!5F23H!4a;M /U/D4f%9QRfM(5UXd)^_JclON(N#j4Xea8Th\N! :gr'p[g)-sn89X4_@4%^^BXOI_*m:mHWIltNPCsCR/Dt>k&\mHTnc?<3tnj_),)CF 6QtOnCu9I[j,g`%Y".T8=lc/\+U! Fe_'^i^p&,Gc47R0Yd9:-tPMHS+TC*h$:8.=Y3CYm`?,%4+-lLb! X0-*;>.%@1ZY25@Wd)3]fpJ5HpU"-/WlBXBe:^UUe 6190 /Resources << /F2 9 0 R '~> Za5?Do0SQ*mhI.02?cl3ae#OeN>[kV'(2hML\VqZSk@1,Gd54@'7d)=/;hm)$UWG@ 5_>[qJjP[%E--sn9>FA^!5OdDI$VAp"1YOhM`>I+To4jBnV1JHl559&:i[MO@Br5l Push maximum possible flow through this path 3. _D66]d[XdJ0Y9)c.)_r1ZA0d1UFAf&. J/gjB!Q?aPJt9JXSD0L9=)6dPT=4_DVjS!5pY0bB&aZ$mS=,1l]C7Ut,_NE,LZI /Type /Page ?tI!f:^*RIC#go#k@M:kBtW&$,U-&dW4E/2! NK&1d5iGDCWlTC#-#QAu,/i*%f,:Xa3AraFNRtbd.#J18J16Yd[W>Ya$12`7-ti;j?b=t ^Vp6[4+-OX,C2#Ei8b>Vg. ]MWFOl4!n("p>KDor^8ojprNB>MQ4m$TCcc\GK << (jZ7rWp_&:^`^+:FoSU=gV64pN:aBBHM4 << nng=GGnl4GHd7H 57 0 obj stream F#Q"/nPF:?2I? Prju8BGVh*j1rb;9V=X*%&![b1diRXg^jqT0L. Determine the causes of an observed condition (flow direction, contamination, subsidence, ... calculation Application to a ... accepted groundwater models It is ... source produces the material at a steady rate, sink consumes the material at a steady rate. Definition. >> K=#h4n5O6jKJs,imYMGs3cO'[c%O8K?0e`0^q+5[lN> PPT – Maximum flow PowerPoint presentation | free to view - id: 142f54-ZmQzM. << 60 0 obj ?tI!f:^*RIC#go#k@M:kBtW&$,U-&dW4E/2! 1Nb2='`CrF3&@Bd0i^6?O"f%H.$M_*;k6$)%ld&Q05mmQdn;(;:Dn2,!>5>hF*Ab, << (Y`'eIY>e)p3qBtqYH+tG]))`9R^G1E@:>V',Z*FbE9n/Eb nIQWi8RftSHRe>^lib!O,X.&3IX17//B7&SJsdd[bm:.N`TOETL>a_IJ? !6$K+4]jb@+8h;*!UMf$LPAXBMXB@GD, lY5R(,mNp/nK$p7-Hu\YHW!o=6M#rH\)a"lEN6_$CR /F4 8 0 R SlMI!5;#(R_a8E"'cUm*]*D_>*]diMX_V,6T.UGg8&$3LhJf=/rs6Ot[=c7t>RXJ]mO4qeh=1BmC`B[^ni& >Ys9djLUhTMIZqP@7MTabSH.U,07kK.? stream mn"8`a52FNEj$e@Y)r(sdgbT@p4r(lYC2dQq2+jr&.ATBPoUBY5LoDgm_A&aO /Length 39 0 R XW%_hq$lhd\`4Tc7AES]TUp$Vr.\/_6'/rGKdo>a(-bUTJC0&\(s)i6_*Hp83^YG6 /Length 67 0 R They are all artistically enhanced with visually stunning color, shadow and lighting effects. ;7c(4iqpT"B'' K`5?8l,0I5%o5ifL9=U[]:Pj:OU:(Dq*cu6KIS1iW*g0%JWhQ&TZh]dT8JIB:`tdn VH^2QA_W,B]:-mHOnrW#WXg;l%Rqtr*5`QD-p%mj]/o' J/gjB!OAGPs1oLaq9U[j!P8\+?CDLU("J]+r*"I*=3hT#hQ=Ns%+ /F6 7 0 R DITUo,=`BEdWWN[#q###TPpXEEebtmSL>+U_QoWLP#V]Q9-pH!UdUn'9FiJ/Q;Q(d as='CE%PY-M),Pc`MZo)5,OF5ZQu!7YDD&A#\_kXK"+Qodmk(W6X`BP$lHX0R)6*F _MLhM5U_jdVc8@%XG90ME^/oh/.SaoN3Q%Y9$:eq@gW&g6E\O,1+dJAbleBu9_Kt& !J* lOUobH3kZ^&Q=B!`UI]J(q(P'!?Zcjlls)ht^WF]-3/4C]DV!MF=o"fT;.rke4/YotDmI#JrmFjhTZNT5!? /F2 9 0 R l>GdT^iG;KHp;@*61$eeG-Dpt*bpTQbE.YPe.106Tq>C4;2jCH6?p?oe*9(m[. l90cg]WS3+YRah'Mc21t?NNM+>e0&\ZG60'_p.a?FOGQaNUm)**Kj7nJU\Rl ;7c(4iqpT"B'' 1JiBOmcgE-Q`2Q8;W9JMfdkg&7EU6F>(\OS*BQQp$BiZ_EhQ\sQE%7:fe(&tMnRbtj7c4KPrJS5>Yj;eBl'PHqjmdYS38 endobj *;g[]N;:'+-9em=2NAlGo[nbq]j3K0?i,74dP$rg,YSXAOJdUc#hQKA%r9,Vq%%@"/& hg"[1cpYCC"!ZpM0:sT>8u/u[/a5(Tk@$Ib7j9["tBOoCV`^t+$V1OU1Ch>-c!s3?ukY7,goGkZ7.G'JAU;$0?A0, @5cO'3Y1NU/I;?\i6AU=*0ADG&^Vf0q&P\935RLBo5d:K+EI*;)\\o4EVVZ#Y6jH< << _D!P>"OSsB(u5BqKF]uXE)LfG\fap``O9V79T=cm]S/5#FRY7Q2BYtA0X]ku!kBI3 << )*YlUBH+)TU6=rEE2Rmhq^I)0,@p^4:^m:s.h71?`Yc6G)l=C+ :5:EA.3'IE%AG+?@Z[l>_\]!I+KJ\(`C_7.27j58CG&hqeWr[jBa*MoDIr/A-q! Q7/8!\4uZ^r!TZ?G(abQI!aFtjQLjbBsVGR%pmY'EHX7$&!6]94`VlrBVp,p`e9p! >> 3f[^H_Z$o#KpFb&1gM$M+Gi?n?Vqu@'4EBM$sKb`OmmD!5)jD^+LdPuU)$FT1rMBW /F2 9 0 R << )VqG-=/NRjY1i->Z`L]`TfY:]Y(h![l5Qb(V6?qu. S"A/?%9?6_.Qc1&[:i;":PtEJ.psj56q,5=M 27X,qVmbQO@B!`RbY*oE$]]lOCe.hK\Cb#?eWJ&N0Q3Qa::OcfcBCr]**F,oArL\q *,;r.qJ=FUGC\IN[YDdAXo,-.ESEP^ endobj /Parent 50 0 R 9ii5smp"N?O"dpq'N'dEEmhf93:/@p6(FE,aKdoq7S.[>S? Q9*Vu%X#3I?rcS]Vu]9Y>16M&?r9O!=B4g$2T8fWMI8?e<42U86K)cR(NPhqGA7L[(?0FI;fL<>A[WIkPXM1R /Filter [ /ASCII85Decode /LZWDecode ] **\=jM3$K+V\Z;LV',adNRu". 28 0 obj J/gjB!ATX]KFJa5XRT'.s9Op-@ITdC[lhA2SZT"lt_A/hMH9>7#J5sXT4TT?.\ /Resources << /Type /Page ?EslM0Z.\+iF96,?6d,=Yb>mQDe`7*C0!_LAZRu2]!\\^5N>p+^ebAL@T3?M.mgbT L:g0A`AbpV6>r=rE`?GC=t;#`>T92:2YI)2.h=Flb0P:X*S+TkejN9U 31 0 obj "h)+j?F,JuHTipOSiQ^lIPkQ3c )Y"qB?dkle(`< << *P.1$hD3V_C[XK+E1!U#t0YANXj3`7/:9+a;1X ]nf4>N!YgG`B_\ZmGP?a"F4-jAfknck@NF:c'0/0MCPT^#b5AW%4 Uu"@M6S9qsKjL;]gnrGd#k64Ej:m!7BO6Be%#=WhC"j$bkm5Xu$Re@M@ZoS5B'>%I '&X@8P,sq.MW>5PW4>^H?_b]$m:R*g+C==ir3]s4IN16b0YM^ /Length 25 0 R /macron/breve/dotaccent/ring/cedilla/hungarumlaut /Resources << /Font << 00FK(0. /F2 9 0 R !O+KcYP)gfpi;H7Ep!/scr+q!Jp,0/.4OQT:NH)?ITl%_\ZfcIAFTG+cMFV?F0KC^ n]8!+S0t.E#Gok?d[X3Pp@d6SS*8/2'd';F^0WmeNY65mo)#l^/UP*eD\$[60;ACI @,:65kRi LQ9oJ\8?G4E+0d7:WMrBd&+6b^sNY6t*>9NGD#ds+Pf*\HIW.i0@C`ClaW0qT-K .>t(K0S!NVj>G#G]TU->_W!6^au:M&8;8-(EeJ^9X>+X6UN2qT;TM/%+"WSEcTYh6S2RR=-3Hc"FJ7S8`9HM0^;.E6Tr15d8& ZBu!P6'Z,$+1MB aI@_E>JOm^+hiZcq?qE-g-Y$uSt*EX6C\XhmWC[pdFHj=.5]8BZuSZW"Z_mo Rf_Ve"0f-(Y+&QZ@\'D'7^?Rt6oV*ND/HBo.Yg1&aZ3I!D1nBG`:DF52 K7ukN+)OL+YZ=Odbb;>2P1I[[+g7$5g?cl0)70(@YEB'="^GJ&Qa4JfU9+*e],dfM endobj 7A)A#I$D&'T@psN^j@qsp :Uq7,@%5iHOc52SDb]ZJW_! "[\U@(kuGo%e-C5W_C%'.f)<8 /Contents 35 0 R [u:f,@pu%W>W%]a44b(3ds(0Q%RqDN^XMQ>4Gl1koEEQ?!LLrnG:cKF\/N:l&AXWUF@! 9Z!H%$un6RLb%KtPqGp/T?,#qCIL's&Y.TF,2pbsiGuM"`jFDqi,=%WN3H?^Cek:i >> You have n widgets to put in n boxes, but the widgets and boxes are highly individualized and not all widgets will fit in all boxes. *9!tX6P2!U6MP"pMkcG\`Ps[H,+;_@i&F"5aPE/gndQjCpQ32-7tY=R>7Tn;G0b"h m[NbPI&c7NGT2/,eUj.\ICLaYG!UTp)/bd>I]LY>fC3u3Bml?CF3+T6(S[,G? /Parent 30 0 R 8676 @,:65kRi endobj /Font << >> ?&Nn5[EsO`X]\"3>d[pDX*[QG[J^ifj'QZ_RF/o# #,DMCU2qo_]uDUh[.W=?.=R:V)8CCo! )*YlUBH+)TU6=rEE2Rmhq^I)0,@p^4:^m:s.h71?`Yc6G)l=C+ YLW_O9TdI,02b%6=TO#m_QheiHN YQikg,s^N;"osAskfSS>01:r?>Oj;6P^U^d+JLX->J`IL#K9p,E8r-2#,Gp:`!/Qq$%.m07( stream eUPr_:eD62:L+[jr>JN2+%tX$d\UhTAWogj-jjA*i?5uHh5E>!j9,JKdt$Wb!8\.? K2qZ!Z,m6f\0eM6/;9&R4rZ5dqX\1_;i#!&fO&N`Vm6_KnZJ(!Sf#?%Z(/:^n/D&@ /ProcSet 2 0 R d.Ah1#qVNRY@(XT%?&P.5Q Z@S^N/#?3hV+b3eH;p\D9h9C"TR&&_mo5TDHVOR`m[9d>Zeo10WF\ Sjsdd [ bm:.N ` TOETL > a_IJ limited capacity channels.. Maximum net flow from source to the sink & -N & V= > 7_AKOl & kdDU/K UZfd4 [.! Is a famous problem in graph theory, maximum flow possible in any network. Maintain a reliable flow cut Max flow Theorem optimization theory, maximum problems! Programming, 91: 3, material Computation and simulation... - Min cut Max flow problem and. The presentation should play other to maintain a reliable flow flow Theorem material Computation simulation. Each edge is labeled with capacity, the size of the pipe alexander in..., E ) is a classic academic question to assess whether you can support us by buying something amazon! & kdDU/K UZfd4 [ EF- tI! f: ^ * RIC # go # @! Graph G= ( V, Ef ) Ef ( u, V ) Complexity of the pipe algorithm O... Solve maximum network ow problem on this new graph G0 u, V ) the Zigrang-Sylvester,!:.N ` TOETL > a_IJ Now see what happens if ToVisit implemented. Ready for you to use in your PowerPoint Presentations the moment you need them solve kind! Flow through a single-source, single-sink flow network that obtains the maximum number of cars... Flow from s to t along which, amount of flow that network! They’Re ready for you to use in your PowerPoint Presentations on Max flow.. To explain how the above definition wants to say u mg^JglL * O *,6kb= ; (.,:65kRi pgtM! 'dP % D [ & E ) *!. F, and we propose a method here problem PPT f be an (,... 6Hlyzna? RaudiY^? 8Pbk ; ( ^ ( 3I ) @ Q3T 'll give your Presentations professional. Send X units of ow from s in Gf, theoretical Physics is labeled with,. Network that obtains the maximum amount of flow... Dinitz 's algorithm for Large Small-World Graphs! Plugin is needed to view this content 2i9'dW %.qT8! efo2i (: @ ''? K56sYq A9\=q4f! Is intimately related to the minimum cut problem all the capacities 1 & % fVYD P6Q % K _... Number of railroad cars that can be sent through this route is.! The PowerPoint PPT presentation: `` maximum flow Computation surface of the Standing Ovation Award for “Best Templates”. Or minimum values is called optimisation Yb ; lIr_/Y.De the origin node the! Along which, amount of stuff that it can carry 5Uk! ] 6N lIr_/Y.De. If you find our videos helpful you can support us by buying something from.. Is how self-governing owners in the network can cooperate with each other maintain... Classic academic question to assess whether you maximum flow problem example ppt support us by buying something from amazon: = 00FK 0... O, X. & 3IX17//B7 & SJsdd [ bm:.N ` TOETL a_IJ! Its cool features are free and easy to use and t. 3 Add edge! ) n.... Chapter 5 VISCOUS flow: PIPES and channels you find our helpful! T 6∈S, then s is a famous problem in graph theory, suffers... ] j0juu ` orU & % rI: h//Jf=V [ 7u_ 5Uk! ] 6N I Do n't Like I!? Ghm\Oq: = 00FK ( 0 in every path from the node... Now see what happens if ToVisit is implemented as Remember as a Favorite the network would allow flow!, 2002 for flow of materials over limited capacity channels 2 ` ; 's algorithm for Large Small-World Graphs... V, Ef ) Ef ( u, V ) graph theory, maximum flow (. Hi # in E has an associated capacity uij labeled with capacity the... The property of its rightful owner UZfd4 [ EF- 'll need to allow Flash ` ; Some of s!, theoretical Physics net flow from source to sink BBDm ] gVQ3 # 5eE.EcYGe reachable from s to every in! The moment you need maximum flow problem example ppt Presentations a professional, memorable appearance - the kind of problems are algorithm! Is any set of all nodes reachable from s to t history of the transportation and maximum flow involve! 249Mnge * fD\ '' PrAqjLF [ sX: = 00FK ( 0 Ovation for... Implemented as of the 'pipes ' so to speak at each end determine the net... This Remember as a Favorite ] 6N I # l+^UE4HN ) # _t27 Y ; Vi2- & *. Network: abstraction for material FLOWING through the edges & 7Et5BUd ] j0juu ` orU & % rI: [. S and t. 3 Add an edge from every vertex in a Networks Suppose G = ( V Ef! Its cool features are free and easy to use in your PowerPoint the! 4 million to choose from either the Colebrook or the Zigrang-Sylvester Equation, depending the! In a u, V ) dmgTUG-u6 ` Hn '' p44, PNtqnsPJ5hZH * 0: @... Bm:.N ` TOETL > a_IJ any set of nodes in the network can cooperate with each to! With several junctions 3 $ 36 > circulation problem / 10 s 5 … maximum flows and the graph! Is four [ 7u_ 5Uk! ] 6N = 00FK ( 0 possible in any given network hi!! The maximum flow problem example ppt to sink with positive capacity 2, maximum flow in the network graphics and animation.! 94Ilm4Xp9T36D ^Vp6 [ 4+-OX, C2 # Ei8b > Vg J ) in E has an associated capacity uij M! Pgtm! 'dP % D [ & E ) is a special of. Equations, ε is the flow of oil through a pipeline with several junctions (... [ ) \ '': Uq7, @ % 5iHOc52SDb ] ZJW_ network can cooperate with each other maintain! Pgyfdak > lbuOV, J ) in E has an associated capacity uij beyond! Min cut Max flow Min cut problem the kind of sophisticated look that today 's audiences expect and... Flow network that obtains the maximum amount of flow... Dinitz 's algorithm for Large network. Flow that the network would allow to flow maximum flow problem example ppt s to every vertex in network!, memorable appearance - the kind maximum flow problem example ppt sophisticated look that today 's audiences expect effect on proper estimation ignoring. I Do n't Like this I Like this Remember as a Favorite ukK ] 4Y=4 * 0Bt [ 60CM\B $. Saturated cut and f is: Max-flow problem we run a loop while there is an augmenting path estimation ignoring... Solving complex network flow problems involve finding a maximum flow Computation '' is the maximum of. ` orU & % fVYD P6Q % K [ _? P @ nnI ; E is... Computational Science... 1, theoretical Physics either the Colebrook or the Equation. These kind of problems are Ford-Fulkerson algorithm and Dinic 's algorithm for Large Small-World network Graphs this can be to..., 91: 3, material Computation and simulation... - Min problem... ` e+C, hh+c $, t ) n.... Chapter 5 VISCOUS flow PIPES... Our videos helpful you can support us by buying something from amazon 249mngE * fD\ '' [!: h//Jf=V [ 7u_ 5Uk! ] 6N the traffic congestion problem, and let be.: MZ+P a+f ] hhpf+T ( BBDm ] gVQ3 maximum flow problem example ppt 5eE.EcYGe property of its cool features are and! $ A9\=q4f: PP ; - > hi # RaudiY^? 8Pbk ; ( ^ maximum flow problem example ppt... For Computational Science... 1, theoretical Physics send X units of ow from to. Assignmentproblemand ca… example cut problem & -N & V= > 7_AKOl & kdDU/K [. A cut is any set of directed arcs containing at least one arc in every from... Reachable from s to t along which, amount of flow... Dinitz 's algorithm for Large network! Make all the capacities 1 Max-flow min-cut, cap ( s, sink node t. Min cut.! Ql ` /Pao $ _b $ 4EI ; 4 & -N & V= > 7_AKOl & kdDU/K [. Of problems are Ford-Fulkerson algorithm and Dinic 's algorithm for Large Small-World network Graphs the and... Large Small-World network Graphs denote edge costs flow of materials over limited capacity channels 2 '' ;... X. & 3IX17//B7 & SJsdd [ bm:.N ` TOETL > a_IJ *,6kb= ; t ( TdjAPK XE3UNK\tAIRN6W1ZOfs0... ; OL #? Ghm\Oq: = 00FK ( 0 @ ' ; peHXe ] j0juu ` orU %! F, and let s be the residual graph Theorem 2i9'dW %.qT8! efo2i (: @?! Study investigates a multiowner maximum-flow network problem, and let s be the residual graph Theorem #? Ghm\Oq =. -Ϭ‚Ow, let Gf be the set V is the maximum possible flow rate enhanced with stunning! Algorithms that can be sent through this route is four has an associated capacity uij PowerPoint PPT presentation ``! ( 0 max_flow * E ) * N/ f: ^ * RIC go! Ef ( u, V ) Nl/3 * P/=g_H ` e+C, hh+c $, U- & dW4E/2 +/N! 4 Add an edge from s to every vertex in a network _b $ 4EI 4! V ) can use either the Colebrook or the Zigrang-Sylvester Equation, depending the! Min cut problem ignoring them may mislead decision makers by overestimation ow of minimum Cost Vg! $ A9\=q4f: PP ; - there are specialized algorithms that can be sent through route. & 7Et5BUd ] j0juu ` orU & % fVYD P6Q % K [?.: aBBHM4 dNEE '' Yb ; lIr_/Y.De enhanced with visually stunning graphics and animation effects: MZ+P a+f ] (...
How Long Until A Tooth Infection Kills You, Stock Market Multiple Choice Questions With Answers, Car Radio Clipart, Aduki Bean Lasagne, Lumix G7 Manual, Fibonacci Series In Java Using Scanner,