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On Approximability of Connected Path Vertex Cover

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Approximation and Online Algorithms (WAOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10787))

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Abstract

This paper is concerned with the approximation complexity of the Connected Path Vertex Cover problem. The problem is a connected variant of the more basic problem of path vertex cover; in k-Path Vertex Cover it is required to compute a minimum vertex set \(C\subseteq V\) in a given undirected graph \(G=(V,E)\) such that no path on k vertices remains when all the vertices in C are removed from G. Connected k-Path Vertex Cover (k-CPVC) additionally requires C to induce a connected subgraph in G.

Previously, k-CPVC in the unweighted case was known approximable within \(k^2\), or within k assuming that the girth of G is at least k, and no approximation results have been reported on the weighted case of general graphs. It will be shown that (1) unweighted k-CPVC is approximable within k without any assumption on graphs, and (2) weighted k-CPVC is as hard to approximate as the weighted set cover is, but approximable within \(1.35\ln n+3\) for \(k\le 3\).

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Notes

  1. 1.

    A related notion of proper matchings was used in [26].

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Acknowledgments

The author is grateful to the anonymous referees for a number of valuable comments and suggestions. This work is supported in part by JSPS KAKENHI under Grant Numbers 26330010 and 17K00013.

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Authors and Affiliations

  1. Toyohashi University of Technology, Toyohashi, 441-8580, Japan

    Toshihiro Fujito

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  1. Toshihiro Fujito
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Correspondence to Toshihiro Fujito .

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  1. The University of Western Ontario, London, Ontario, Canada

    Roberto Solis-Oba

  2. German University of Technology in Oman, Muscat, Oman

    Rudolf Fleischer

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Fujito, T. (2018). On Approximability of Connected Path Vertex Cover. In: Solis-Oba, R., Fleischer, R. (eds) Approximation and Online Algorithms. WAOA 2017. Lecture Notes in Computer Science(), vol 10787. Springer, Cham. https://doi.org/10.1007/978-3-319-89441-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-89441-6_2

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