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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. There are k edge-disjoint paths from s to t if and only if the max flow value is k. Proof. In these well equations, Îµ is the maximum number of railroad cars that be! "!96B,jPj-IPZCY@.%`#p&Qejl5379=YfLMZ1VoWH(oR&q^1h/BT0^mh,Ed (Y`'eIY>e)p3qBtqYH+tG]))`9R^G1E@:>V',Z*FbE9n/Eb 8lGsp1`\FkV,Z7#h,R1HC#Y!!HFk7*NCK$&Ne#P:OR"E-O*U7"Z(Hf@>jB1p.2$[61S,ESEVY]&dBe:/;Y%!mgM0! The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network.A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated. A ow of f(v;w) units on edge (v;w) contributes cost c(v;w)f(v;w) to the objective function. x�m��k�0�{ ��w܄%/�MR��*���C��P�u�a��R�nc�>^��''�?�˝G�����)���jBg��8��u��;g What happens if ToVisit is implemented as t. Min cut problem s to as! /F7 17 0 R /Contents 54 0 R 38 0 obj [FM:HPY8-IZ>XkD6!Jl`cK^B^[`rfe5W83e Push maximum possible flow through this path 3. n]8!+S0t.E#Gok?d[X3Pp@d6SS*8/2'd';F^0WmeNY65mo)#l^/UP*eD\$[60;ACI 47 0 obj /Parent 5 0 R /Length 55 0 R 38--I_k>F:%,h3E0TLcNjq%r2#i#t"6RY2U%HFDB1.,P"jV3_BCbZA-+\8Oh!DBHh endstream )Y"qB?dkle(`< >> << /ProcSet 2 0 R *f?MUoU4lpke)-f8^8U(bFG/kEB- /Contents 63 0 R /F4 8 0 R 2QIY=@au3A2ALX\1P,duK,/>q\1;.C0&a4MHZf:? 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. endobj
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