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European Symposium on Algorithms

ESA 2009: Algorithms - ESA 2009 pp 647–658Cite as

Constant Ratio Fixed-Parameter Approximation of the Edge Multicut Problem

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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(k)·n 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.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Hungary

    Dániel Marx

  2. Cork Constraint Computation Centre, University College Cork, Republic of Ireland

    Igor Razgon

Authors
  1. Dániel Marx
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  2. Igor Razgon
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Editor information

Editors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Amos Fiat

  2. Fakultät für Informatik, Universität Karlsruhe (TH), Am Fasanengarten 5, 76131, Karlsruhe, Germany

    Peter Sanders

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Marx, D., Razgon, I. (2009). Constant Ratio Fixed-Parameter Approximation of the Edge Multicut Problem. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_58

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  • DOI: https://doi.org/10.1007/978-3-642-04128-0_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04127-3

  • Online ISBN: 978-3-642-04128-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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