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On Approximability of Connected Path Vertex Cover

  • Toshihiro FujitoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10787)

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 \(k\le 3\).

Keywords

Connected Path Vertex Cover Approximation algorithms Connected vertex cover 

Notes

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Toyohashi University of TechnologyToyohashiJapan

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