Constant Ratio Fixed-Parameter Approximation of the Edge Multicut Problem

  • Dániel Marx
  • Igor Razgon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)

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(knO(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 present paper is introducing the first natural W[1]-hard problem that is constant-ratio fixed-parameter approximable.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Dániel Marx
    • 1
  • Igor Razgon
    • 2
  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsHungary
  2. 2.Cork Constraint Computation CentreUniversity College CorkRepublic of Ireland

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