Maximum Flows 6 . 1 The Maximum Flow Problem
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چکیده
6.1 The Maximum Flow Problem In this section we define a flow network and setup the problem we are trying to solve in this lecture: the maximum flow problem. Definition 1 A network is a directed graph G = (V,E) with a source vertex s ∈ V and a sink vertex t ∈ V . Each edge = (v, w) from v to w has a defined capacity, denoted by u(e) or u(v, w). It is useful to also define capacity for any pair of vertices (v, w), with u(v, w) = 0 for any pair (v, w) ∈ E. Let m = |E| and n = |V | be the number of edges and vertices in the graph, respectively.
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