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Deterministic Parameterized Connected Vertex Cover

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Algorithm Theory – SWAT 2012 (SWAT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7357))

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Abstract

In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and such that X induces a connected subgraph. For this problem we present a deterministic algorithm running in O(2kpoly(n)) time and polynomial space, improving over the previous-best O(2.4882kpoly(n)) time deterministic algorithm and O(2kpoly(n)) time randomized algorithm. Furthermore, when usage of exponential space is allowed, we present an O(2k k(n + m)) time algorithm that solves a more general variant with real weights.

Finally, we show that in O(2kpoly(n)) time and space one can count the number of connected vertex covers of size at most k, and this time upper bound can not be improved to O((2 − ε)kpoly(n)) for any ε > 0 under the Strong Exponential Time Hypothesis, as shown by Cygan et al. [CCC’12].

The author is partially supported by ERC Starting Grant NEWNET 279352, NCN grant N206567140 and Foundation for Polish Science.

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Author information

Authors and Affiliations

  1. IDSIA, University of Lugano, Switzerland

    Marek Cygan

Authors
  1. Marek Cygan
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Editors and Affiliations

  1. Institute of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Department of Information and Computer Science, Aalto University, PO Box 15400, 00076, Aalto, Finland

    Petteri Kaski

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Cygan, M. (2012). Deterministic Parameterized Connected Vertex Cover. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-31155-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31154-3

  • Online ISBN: 978-3-642-31155-0

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