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Clique Cover and Graph Separation: New Incompressibility Results

Published:01 May 2014Publication History
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Abstract

The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. In this article, we show that, unless the polynomial hierarchy collapses to its third level, the following parameterized problems do not admit a polynomial-time preprocessing algorithm that reduces the size of an instance to polynomial in the parameter:

---Edge Clique Cover, parameterized by the number of cliques, ---Directed Edge/Vertex Multiway Cut, parameterized by the size of the cutset, even in the case of two terminals, ---Edge/Vertex Multicut, parameterized by the size of the cutset, and ---k-Way Cut, parameterized by the size of the cutset.

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      • Published in

        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 6, Issue 2
        May 2014
        98 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/2631196
        Issue’s Table of Contents

        Copyright © 2014 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 May 2014
        • Accepted: 1 March 2014
        • Revised: 1 February 2014
        • Received: 1 January 2013
        Published in toct Volume 6, Issue 2

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