Approximating generalized multicut on trees

Abstract

Given a tree T with costs on edges and a collection of terminal sets X = {S1, S2, . . ., Sl}, the generalized Multicut problem asks to find a set of edges on T whose removal cuts every terminal set in X, such that the total cost of the edges is minimized. The standard version of the problem can be approximately solved by reducing it to the classical Multicut on trees problem. For the prize-collecting version of the problem, we give a primal-dual 3-approximation algorithm and a randomized 2.55-approximation algorithm (the latter can be derandomized). For the k-version of the problem, we show an interesting relation between the problem and the Densest k-Subgraph problem, implying that approximating the k-version of the problem within O(n1/6-ε) for some small ε > 0 is hard. We also give a min{2(l - k + 1), k}-approximation algorithm for the k-version of the problem via a nonuniform approach. © Springer-Verlag Berlin Heidelberg 2007.