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Saving on Phases: Parameterized Approximation for Total Vertex Cover

  • Henning Fernau
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Henning Fernau
    • 1
  1. 1.Abteilung InformatikUniversität TrierTrierGermany

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