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Fast and Simple Local Algorithms for 2-Edge Dominating Sets and 3-Total Vertex Covers

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WALCOM: Algorithms and Computation (WALCOM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9627))

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Abstract

A local algorithm is a deterministic (i.e., non-randomized) distributed algorithm in an anonymous port-numbered network running in a constant number of synchronous rounds, and this work studies the approximation performance of such algorithms. The problems treated are b-edge dominating set (b-EDS) that is a multiple domination version of the edge dominating set (EDS) problem, and t-total vertex cover (t-TVC) that is a variant of the vertex cover problem with a clustering property. After observing that EDS and 2-TVC are approximable within 4 and 3, respectively, using a single run of the local algorithm for finding a maximal matching in a bicolored graph, it will be seen that running the maximal matching local algorithm for bicolored graph twice, 2-EDS and 3-TVC can be approximated within factors 2 and 3, respectively.

T. Fujito—Supported in part by the Kayamori Foundation of Informational Science Advancement and a Grant in Aid for Scientific Research of the Ministry of Education, Science, Sports and Culture of Japan.

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Acknowledgments

The authors are very grateful to the anonymous referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Toyohashi University of Technology, Toyohashi, 441-8580, Japan

    Toshihiro Fujito & Daichi Suzuki

Authors
  1. Toshihiro Fujito
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  2. Daichi Suzuki
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Correspondence to Toshihiro Fujito .

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Editors and Affiliations

  1. Dept. of Computer Science and Engin., Bangladesh Univ. of Engin. & Technol., Dhaka, Bangladesh

    Mohammad Kaykobad

  2. Dept. of Computer Science, Sapienza University of Rome, Rome, Italy

    Rossella Petreschi

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Fujito, T., Suzuki, D. (2016). Fast and Simple Local Algorithms for 2-Edge Dominating Sets and 3-Total Vertex Covers. In: Kaykobad, M., Petreschi, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2016. Lecture Notes in Computer Science(), vol 9627. Springer, Cham. https://doi.org/10.1007/978-3-319-30139-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-30139-6_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30138-9

  • Online ISBN: 978-3-319-30139-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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