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On Cutwidth Parameterized by Vertex Cover

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Parameterized and Exact Computation (IPEC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7112))

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Abstract

We study the Cutwidth problem, where input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two consecutive vertices. We give an algorithm for Cutwidth with running time O(2k n O(1)). Here k is the size of a minimum vertex cover of the input graph G, and n is the number of vertices in G. Our algorithm gives an O(2n/2 n O(1)) time algorithm for Cutwidth on bipartite graphs as a corollary. This is the first non-trivial exact exponential time algorithm for Cutwidth on a graph class where the problem remains NP-complete. Additionally, we show that Cutwidth parameterized by the size of the minimum vertex cover of the input graph does not admit a polynomial kernel unless \(\ensuremath{\textrm{NP} \subseteq \textrm{coNP}/\textrm{poly}}\). Our kernelization lower bound contrasts the recent result of Bodlaender et al.[ICALP 2011] that Treewidth parameterized by vertex cover does admit a polynomial kernel.

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Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Poland

    Marek Cygan, Marcin Pilipczuk & Michał Pilipczuk

  2. University of California, San Diego, La Jolla, CA, 92093-0404, USA

    Daniel Lokshtanov

  3. The Institute of Mathematical Sciences, Chennai, 600113, India

    Saket Saurabh

Authors
  1. Marek Cygan
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  2. Daniel Lokshtanov
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  3. Marcin Pilipczuk
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  4. Michał Pilipczuk
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  5. Saket Saurabh
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Editors and Affiliations

  1. MTA SZTAKI, Lágymányosi u. 11, 1111, Budapest, Hungary

    Dániel Marx

  2. Lehrgebiet Theoretische Informatik, RWTH Aachen, Ahornstraße 55, 52056, Aachen, Germany

    Peter Rossmanith

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Cygan, M., Lokshtanov, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S. (2012). On Cutwidth Parameterized by Vertex Cover. In: Marx, D., Rossmanith, P. (eds) Parameterized and Exact Computation. IPEC 2011. Lecture Notes in Computer Science, vol 7112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28050-4_20

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  • DOI: https://doi.org/10.1007/978-3-642-28050-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28049-8

  • Online ISBN: 978-3-642-28050-4

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