Optimal Partition of a Tree with Social Distance

  • Masahiro OkuboEmail author
  • Tesshu HanakaEmail author
  • Hirotaka OnoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)


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.


Graph algorithm Tree Graph partition Social distance 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of InformaticsNagoya UniversityNagoyaJapan
  2. 2.Department of Information and System EngineeringChuo UniversityTokyoJapan

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