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Probabilistic Local Majority Voting for the Agreement Problem on Finite Graphs

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Book cover Computing and Combinatorics (COCOON 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1627))

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Abstract

Motivated by the study of the deterministic local majority polling game by Peleg et al., this paper investigates a repetitive probabilistic local majority polling game on a finite connected graph by formulating it as a Markov chain. We mainly investigate the probability that the system reaches a given absorbing state and characterize when the probability attains the maximum (and minimum).

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References

  1. J-C. Bermond and D. Peleg, “The power of small coalitions in graphs,” Proc. 2nd Structural Information & Communication Complexity, Olympia, Greece, Carleton Univ. Press, 173–184, 1995.

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  2. W. Feller, “An Introduction to Probability Theory and its Applications Vol. I (3rd ed.),” New York: John Wiley & Sons, 1950.

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  3. Y. Hassin and D. Peleg, “Distributed probabilistic polling and applications to proportionate agreement,” Proc. 26th International Colloquium on Automata, Languages, and Programming, Prague, Czech Republic, July 1999 (to appear).

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  4. N. Linial, D. Peleg, Y. Rabinovich and M. Saks, “Sphere packing and local majorities in graphs,” Proc. 2nd Israel Symposium on Theoretical Computer Science, IEEE Computer Soc. Press, 141–149, 1993.

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  5. D. Peleg, “Local majority voting, small coalitions and controlling monopolies in graphs: A review,” Technical Report, Weizmann Institute, 1996. http://www.wisdom.weizmann.ac.il/Papers/trs/CS96-12/abstract.html

  6. D. Peleg, “Size bounds for dynamic monopolies,” Discrete Applied Mathematics, 86, 263–273, 1998.

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Author information

Authors and Affiliations

  1. Department of Information Education, Fukuoka University of Education, Akama Munakata, Fukuoka, 811-4192, Japan

    Toshio Nakata

  2. Department of Computer Science and Communication Engineering, Kyushu University, Hakozaki Higashi-ku, Fukuoka, 812-8581, Japan

    Hiroshi Imahayashi & Masafumi Yamashita

Authors
  1. Toshio Nakata
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  2. Hiroshi Imahayashi
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  3. Masafumi Yamashita
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Editor information

Editors and Affiliations

  1. Department of Information and System Engineering Faculty of Science and Engineering, Chuo University, 1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Takano Asano

  2. Department of Information Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Hideki Imai

  3. Academia Sinica, Institute of Information Science, Nankang, Taipei, Taiwan

    D. T. Lee

  4. Department of Computer Science Faculty of Engineering, Gunma University, 1-5-1 Tenjin-cho, Kiryu, Gunma, 376-8515, Japan

    Shin-ichi Nakano

  5. IBM Tokyo Research Laboratory, 1623-14, Shimo-Tsuruma, Yamato Kanagawa, 242-0001, Japan

    Takeshi Tokuyama

Additional information

Dedicated to Professor Izumi Kubo on occasion of his 60th birthday

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© 1999 Springer-Verlag Berlin Heidelberg

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Nakata, T., Imahayashi, H., Yamashita, M. (1999). Probabilistic Local Majority Voting for the Agreement Problem on Finite Graphs. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_33

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  • DOI: https://doi.org/10.1007/3-540-48686-0_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66200-6

  • Online ISBN: 978-3-540-48686-2

  • eBook Packages: Springer Book Archive

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