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Covering Problems in Edge- and Node-Weighted Graphs

  • Takuro Fukunaga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8503)

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.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Takuro Fukunaga
    • 1
    • 2
  1. 1.National Institute of InformaticsTokyoJapan
  2. 2.JST, ERATO, Kawarabayashi Large Graph ProjectJapan

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