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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 {s 1,t 1}, ..., {s m ,t m }; the task is to remove a minimum set of edges such that s i and t i 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(kn O(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.

Keywords

Satisfying Assignment Terminal Vertex Unique Game Conjecture Iterative Compression Correlation Cluster Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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