Covering problems in edge- and node-weighted graphs
Abstract
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large integrality gap of a natural linear programming (LP) relaxation, LP rounding algorithms based on the relaxation yield poor performance. Here we propose a stronger LP relaxation for the graph covering problem. The proposed relaxation is applied to designing primal-dual algorithms for two fundamental graph covering problems: the prize-collecting edge dominating set problem and the multicut problem in trees. Our algorithms are an exact polynomial-time algorithm for the former problem, and a 2-approximation algorithm for the latter problem, respectively. These results match the currently known best results for purely edge-weighted graphs.
Cite
@article{arxiv.1404.4123,
title = {Covering problems in edge- and node-weighted graphs},
author = {Takuro Fukunaga},
journal= {arXiv preprint arXiv:1404.4123},
year = {2014}
}
Comments
To appear in SWAT 2014