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Covering Problems in Edge- and Node-Weighted Graphs

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Book cover Algorithm Theory – SWAT 2014 (SWAT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8503))

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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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Author information

Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Takuro Fukunaga

  2. JST, ERATO, Kawarabayashi Large Graph Project, Japan

    Takuro Fukunaga

Authors
  1. Takuro Fukunaga
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Editor information

Editors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    R. Ravi

  2. DTU Informatics, 2800, Kongens Lyngby, Denmark

    Inge Li Gørtz

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© 2014 Springer International Publishing Switzerland

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Fukunaga, T. (2014). Covering Problems in Edge- and Node-Weighted Graphs. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_19

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  • DOI: https://doi.org/10.1007/978-3-319-08404-6_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08403-9

  • Online ISBN: 978-3-319-08404-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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