Gruia Cc Alinescu
نویسنده
چکیده
The Multicut problem can be deened as: given a graph G and a collection of pairs of distinct vertices (si; ti) of G, nd a minimum set of edges of G whose removal disconnects each si from the corresponding ti. The fractional Multicut problem is the dual of the well-known Multicommodity Flow problem. Multicut is known to be NP-hard and Max SNP-hard even when the input graph is restricted to being a tree. The main result of the paper is a polynomial-time approximation scheme (PTAS) for Multicut in unweighted graphs with bounded degree and bounded tree-width. That is, for any > 0, we present a polynomial-time (1 +)-approximation algorithm. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provide some hardness results. We prove that Multicut is still NP-hard for binary trees and that it is Max SNP-hard if we relax any of the three condition (unweighted, bounded-degree, bounded tree-width). We also show that some of these results extend to the vertex version of Multicut.
منابع مشابه
On a bidirected relaxation for the MULTIWAY CUT problem
In the Multiway Cut problem, we are given an undirected edge-weighted graph G = (V; E) with c e denoting the cost (weight) of edge e. We are also given a subset S of V , of size k, called the terminals. The objective is to nd a minimum cost set of edges whose removal ensures that the terminals are disconnected. In this paper, we study a bidirected linear programming relaxation of Multiway Cut. ...
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