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Optimal Partition of a Tree with Social Distance

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WALCOM: Algorithms and Computation (WALCOM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11355))

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Abstract

We study the problem to find a partition of a graph G with maximum social welfare based on social distance between vertices in G, called MaxSWP. This problem is known to be NP-hard in general. In this paper, we first give a complete characterization of optimal partitions of trees with small diameters. Then, by utilizing these results, we show that MaxSWP can be solved in linear time for trees. Moreover, we show that MaxSWP is NP-hard even for 4-regular graphs.

This work is supported by JSPS KAKENHI Grant Numbers 17K19960, 17H01698, 18H06469.

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Author information

Authors and Affiliations

  1. Graduate School of Informatics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan

    Masahiro Okubo & Hirotaka Ono

  2. Department of Information and System Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, Japan

    Tesshu Hanaka

Authors
  1. Masahiro Okubo
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  2. Tesshu Hanaka
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  3. Hirotaka Ono
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Corresponding authors

Correspondence to Masahiro Okubo , Tesshu Hanaka or Hirotaka Ono .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Guwahati, Guwahati, India

    Gautam K. Das

  2. Indian Institute of Technology Guwahati, Guwahati, India

    Partha S. Mandal

  3. Indian Statistical Institute, Kolkata, India

    Krishnendu Mukhopadhyaya

  4. Gunma University, Kiryu, Japan

    Shin-ichi Nakano

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Okubo, M., Hanaka, T., Ono, H. (2019). Optimal Partition of a Tree with Social Distance. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_10

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  • DOI: https://doi.org/10.1007/978-3-030-10564-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10563-1

  • Online ISBN: 978-3-030-10564-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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