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    Fixed-parameter tractability of multicut parameterized by the size of the cutset

    Marx, D. and Razgon, Igor (2011) Fixed-parameter tractability of multicut parameterized by the size of the cutset. In: UNSPECIFIED (ed.) Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11. New York, U.S.: ACM Press, pp. 469-478. ISBN 9781450306911.

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    Abstract

    Given an undirected graph $G$, a collection {(s1,t1), ..., (sl,tl)} of pairs of vertices, and an integer p, the Edge Multicut problem ask if there is a set S of at most p edges such that the removal of S disconnects every si from the corresponding ti. Vertex Multicut is the analogous problem where S is a set of at most p vertices. Our main result is that both problems can be solved in time 2O(p3) ⋅ nO(1), i.e., fixed-parameter tractable parameterized by the size p of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f(p) ⋅ nO(1) exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.

    Metadata

    Item Type: Book Section
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Administrator
    Date Deposited: 11 Jun 2013 12:41
    Last Modified: 11 Jun 2013 12:41
    URI: http://eprints.bbk.ac.uk/id/eprint/7444

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