LP Relaxation , Rounding , and Randomized Rounding
نویسنده
چکیده
1.1 Max-flow min-cut A flow network is a directed graph D = (V,E) with two distinguished vertices s and t called the source and the sink, respectively. Moreover, each arc (u, v) ∈ E has a certain capacity c(u, v) ≥ 0 assigned to it. Let X be a proper non-empty subset of V . Let X̄ := V −X , then the pair (X, X̄) forms a partition of V , called a cut of D. The set of arcs of D going from X to X̄ is called an edge cut of G, denoted by [X, X̄]. A source/sink cut of a network D is a cut (S, T ) with s ∈ S and t ∈ T . (Note that, implicitly T = S̄.) Given a source/sink cut (S, T ), the capacity of the cut, denoted by cap(S, T ) is the total capacity of edges leaving S: cap(S, T ) := ∑
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