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International Workshop on Combinatorial Algorithms

IWOCA 2012: Combinatorial Algorithms pp 20–31Cite as

Saving on Phases: Parameterized Approximation for Total Vertex Cover

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7643))

Abstract

Vertex Cover and its variants have always been in the focus of study of Parameterized Algorithmics. This can be also claimed for the emergent area of Parameterized Approximation. While Vertex Cover is known to be solvable in time \(\mathcal{O}^*(c^k)\) with some c < 2, this is not the case for variants like Connected Vertex Cover and others that impose some connectivity requirements on the desired cover. The reason behind is the two-phase approach that is taken for this kind of problems. We show that this barrier can be overcome when we are only interested in approximate solutions. More specifically, we prove that a factor-1.5 approximative solution for Total Vertex Cover can be found in time \(\mathcal{O}^*(1.151^{k})\), where k is some bound on the optimum solution.

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Author information

Authors and Affiliations

  1. Abteilung Informatik, Universität Trier, Fachbereich 4, 54286, Trier, Germany

    Henning Fernau

Authors
  1. Henning Fernau
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Editor information

Editors and Affiliations

  1. Kalasalingam University, Anand Nagar, 626 126, Krishanakoil, Tamil Nadu, India

    S. Arumugam

  2. Algorithms Research Group, Department of Computing & Software, McMaster University, L8S 4K1, Hamilton, ON, Canada

    W. F. Smyth

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© 2012 Springer-Verlag Berlin Heidelberg

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Fernau, H. (2012). Saving on Phases: Parameterized Approximation for Total Vertex Cover. In: Arumugam, S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2012. Lecture Notes in Computer Science, vol 7643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35926-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-35926-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35925-5

  • Online ISBN: 978-3-642-35926-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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