Cs 598csc: Approximation Algorithms 1 the Multicut Problem
نویسنده
چکیده
In the Multicut problem, we are given a graph G = (V,E), a capacity function that assigns a capacity ce to each edge e, and a set of pairs (s1, t1), ..., (sk, tk). The Multicut problem asks for a minimum capacity set of edges F ⊆ E such that removing the edges in F disconnects si and ti, for all i. Note that the Multicut problem generalizes the Multiway Cut problem that we saw in the last two lectures. In this lecture, we will see a Θ(log k) approximation algorithm for Multicut. Let’s start by giving an LP formulation for the problem. For each edge e, we have a variable de. We interpret each variable de as a distance label for the edge. Let Psi,ti denote the set of all paths between si and ti. We have the following LP for the problem:
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