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Fast Deterministic Distributed Algorithms for Sparse Spanners

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Structural Information and Communication Complexity (SIROCCO 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4056))

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Abstract

This paper concerns the efficient construction of sparse and low stretch spanners for unweighted arbitrary graphs with n nodes. All previous deterministic distributed algorithms, for constant stretch spanner of o(n 2) edges, have a running time Ω(nε) for some constant ε> 0 depending on the stretch. Our deterministic distributed algorithms construct constant stretch spanners of o(n 2) edges in o(n ε) time for any constant ε> 0.

More precisely, in the Linial’s free model, we construct in \(n^{O(1/\sqrt{\log n})}\) time, for every graph, a 5-spanner of O(n 3/2) edges. The result is extended to O( k2.322)-spanners with O(n 1 + 1/k) edges for every parameter k ≥1. If the minimum degree of the graph is \(\Omega(\sqrt{n})\), then, in the same time complexity, a 9-spanner with O(n) edges can be constructed.

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Author information

Authors and Affiliations

  1. LaBRI, Université Bordeaux 1, 351, Cours de la Libération, 33405, Talence, France

    Bilel Derbel & Cyril Gavoille

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  1. Bilel Derbel
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  2. Cyril Gavoille
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Editors and Affiliations

  1. SITE, University of Ottawa, Canada

    Paola Flocchini

  2. Department of Computer Science, University of Liverpool, L69 3BX, Liverpool, UK

    Leszek Gąsieniec

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Derbel, B., Gavoille, C. (2006). Fast Deterministic Distributed Algorithms for Sparse Spanners. In: Flocchini, P., Gąsieniec, L. (eds) Structural Information and Communication Complexity. SIROCCO 2006. Lecture Notes in Computer Science, vol 4056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780823_9

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  • DOI: https://doi.org/10.1007/11780823_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35474-1

  • Online ISBN: 978-3-540-35475-8

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