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Workshop on Combinatorial and Algorithmic Aspects of Networking

CAAN 2004: Combinatorial and Algorithmic Aspects of Networking pp 63–74Cite as

A Distributed Algorithm to Find Hamiltonian Cycles in \(\mathcal{G}(n, p)\) Random Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 3405))

Abstract

In this paper, we present a distributed algorithm to find Hamiltonian cycles in \(\mathcal{G}(n, p)\) graphs. The algorithm works in a synchronous distributed setting. It finds a Hamiltonian cycle in \(\mathcal{G}(n, p)\) with high probability when \(p=\omega(\sqrt{log n}/n^{1/4})\), and terminates in linear worst-case number of pulses, and in expected O(n 3/4 + ε) pulses. The algorithm requires, in each node of the network, only O(n) space and O(n) internal instructions.

This research was partially supported by the EU within the 6th Framework Programme under contract 001907 (DELIS) and by the Spanish CICYT project TIC2002-04498-C05-03 (TRACER).

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Author information

Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles, Bld du Triomphe, CP 212, B-1050, Bruxelles, Belgium

    Eythan Levy & Guy Louchard

  2. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord Ω-227. 08034, Barcelona, Catalonia

    Jordi Petit

Authors
  1. Eythan Levy
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  2. Guy Louchard
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  3. Jordi Petit
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Editor information

Editors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    Alejandro López-Ortiz

  2. Department of Physics and Computer Science, Wilfrid Laurier University, N2L 3C5, Waterloo, Ontario, Canada

    Angèle M. Hamel

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© 2005 Springer-Verlag Berlin Heidelberg

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Levy, E., Louchard, G., Petit, J. (2005). A Distributed Algorithm to Find Hamiltonian Cycles in \(\mathcal{G}(n, p)\) Random Graphs. In: López-Ortiz, A., Hamel, A.M. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2004. Lecture Notes in Computer Science, vol 3405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527954_7

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  • DOI: https://doi.org/10.1007/11527954_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27873-3

  • Online ISBN: 978-3-540-31860-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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