PTAS for minimum weighted connected vertex cover problem with c-local condition in unit disk graphs

Authors:
Lidan Fan;Zhao Zhang;Wei Wang
Affiliations:
College of Science, Xi'an Jiaotong University, Xi'an, China 710049;College of Mathematics and System Sciences, Xinjiang University, Urumqi, China 830046;College of Science, Xi'an Jiaotong University, Xi'an, China 710049
Venue:
Journal of Combinatorial Optimization
Year:
2011

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Abstract

Given a graph G=(V,E) with node weight w:V驴R +, the minimum weighted connected vertex cover problem (MWCVC) is to seek a subset of vertices of the graph with minimum total weight, such that for any edge of the graph, at least one endpoint of the edge is contained in the subset, and the subgraph induced by this subset is connected. In this paper, we study the problem on unit disk graph. A polynomial-time approximation scheme (PTAS) for MWCVC is presented under the condition that the graph is c-local.