On Approximability of Connected Path Vertex Cover
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 \(k\le 3\).
KeywordsConnected Path Vertex Cover Approximation algorithms Connected vertex cover
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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