Optimal Partition of a Tree with Social Distance | SpringerLink
Skip to main content
Springer Nature Link
Log in

Optimal Partition of a Tree with Social Distance

  • Conference paper
  • First Online:
WALCOM: Algorithms and Computation (WALCOM 2019)

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

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Aziz, H., Brandt, F., Seedig, H.G.: Computing desirable partitions in additively separable hedonic games. Artif. Intell. 195, 316–334 (2013)

    Article  MathSciNet  Google Scholar 

  2. Balliu, A., Flammini, M., Melideo, G., Olivetti, D.: Nash stability in social distance games. In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (AAAI 2017), pp. 342–348 (2017)

    Google Scholar 

  3. Balliu, A., Flammini, M., Olivetti, D.: On pareto optimality in social distance games. In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (AAAI 2017), pp. 349–355 (2017)

    Google Scholar 

  4. Brânzei, S., Larson, K.: Social distance games. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011), pp. 91–96 (2011)

    Google Scholar 

  5. Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3), 75–174 (2010)

    Article  MathSciNet  Google Scholar 

  6. Kagawa, S., Okamoto, S., Suh, S., Kondo, Y., Nansai, K.: Finding environmentally important industry clusters: multiway cut approach using nonnegative matrix factorization. Soc. Netw. 35(3), 423–438 (2013)

    Article  Google Scholar 

  7. Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)

    Book  Google Scholar 

  8. Newman, M.E.J.: Spectral methods for community detection and graph partitioning. Phys. Rev. E 88, 042822 (2013)

    Article  Google Scholar 

  9. Okubo, M., Hanaka, T., Ono, H.: Optimal partition of a tree with social distance. CoRR abs/1809.03392 (2018)

    Google Scholar 

  10. Porschen, S., Schmidt, T., Speckenmeyer, E., Wotzlaw, A.: XSAT and NAE-SAT of linear CNF classes. Discrete Appl. Math. 167, 1–14 (2014)

    Article  MathSciNet  Google Scholar 

  11. Rahwan, T., Michalak, T.P., Wooldridge, M., Jennings, N.R.: Coalition structure generation: a survey. Artif. Intell. 229, 139–174 (2015)

    Article  MathSciNet  Google Scholar 

  12. Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007)

    Article  Google Scholar 

  13. Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)

    Article  Google Scholar 

  14. Sless, L., Hazon, N., Kraus, S., Wooldridge, M.: Forming \(k\) coalitions and facilitating relationships in social networks. Artif. Intell. 259, 217–245 (2018)

    Article  MathSciNet  Google Scholar 

Download references

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tesshu Hanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hirotaka Ono
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10563-1

  • Online ISBN: 978-3-030-10564-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation