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Colloquium on Trees in Algebra and Programming

CAAP 1994: Trees in Algebra and Programming — CAAP'94 pp 234–245Cite as

Probabilistic analysis of an election algorithm in a tree

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 787))

Abstract

In this paper we consider the well-known case of election in a tree, and we study the probability for any vertex of a given tree to be elected. In particular, we show that if we consider the probability distribution based on the comparison of the election probabilities of neighbour vertices, there is one or two vertices having the highest probability of being elected. We give a very simple algorithm to compute these vertices, and we prove that in fact they are the medians.

Exact computations are done for special families of trees as filiform trees, wheels and crystals.

This research was supported by EC Cooperative Action IC-1000 (project ALTEC: Algorithms for Future Technologies).

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Author information

Authors and Affiliations

  1. LaBRI, Université Bordeaux I, ENSERB, 351 cours de la Libération, 33405, Talence, France

    Yves Métivier & Nasser Saheb

Authors
  1. Yves Métivier
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  2. Nasser Saheb
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Editor information

Sophie Tison

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© 1994 Springer-Verlag Berlin Heidelberg

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Métivier, Y., Saheb, N. (1994). Probabilistic analysis of an election algorithm in a tree. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017485

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  • DOI: https://doi.org/10.1007/BFb0017485

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57879-6

  • Online ISBN: 978-3-540-48373-1

  • eBook Packages: Springer Book Archive

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