Constant Ratio Fixed-Parameter Approximation of the Edge Multicut Problem

Abstract. The input of the Edge Multicut problem consists of an undirected graph G and pairs of terminals {s1, t1}, . . . , {sm, tm}; the task is to remove a minimum set of edges such that si and ti are disconnected for every 1 ≤ i ≤ m. The parameterized complexity of the problem, parameterized by the maximum number k of edges that are allowed to be removed, is currently open. The main result of the paper is a parameterized 2-approximation algorithm: in time f(k) · nO(1) , we can either find a solution of size 2k or correctly conclude that there is no solution of size k. The proposed algorithm is based on a transformation of the Edge Multicut problem into a variant of parameterized Max-2-SAT problem, where the parameter is related to the number of clauses that are not satisfied. It follows from previous results that the latter problem can be 2-approximated in a fixed-parameter time; on the other hand, we show here that it is W[1]-hard. Thus the additional contribution of the pr...

• Type: Conference
• Year: 2009
• Where: ESA
• Authors: Dániel Marx, Igor Razgon
• Keywords: Algorithms, Edge Multicut Problem, ESA 2009, Parameterized 2-approximation Algorithm, Parameterized Max-2-sat Problem