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A Fast Network-Decomposition Algorithm and Its Applications to Constant-Time Distributed Computation

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Structural Information and Communication Complexity (SIROCCO 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9439))

Abstract

A partition (C 1,C 2,...,C q ) of G = (V,E) into clusters of strong (respectively, weak) diameter d, such that the supergraph obtained by contracting each C i is ℓ-colorable is called a strong (resp., weak) (d, ℓ)-network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Awerbuch et al. showed that strong \((exp\{O(\sqrt{ \log n \log \log n})\}\), \(exp\{O(\sqrt{ \log n \log \log n})\})\)-network-decompositions can be computed in distributed deterministic time \(exp\{O(\sqrt{ \log n \log \log n})\}\). Even more importantly, they demonstrated that network-decompositions can be used for a great variety of applications in the message-passing model of distributed computing. Much more recently Barenboim (2012) devised a distributed randomized constant-time algorithm for computing strong network decompositions with d = O(1). However, the parameter ℓ in his result is O(n 1/2 + ε).

In this paper we drastically improve the result of Barenboim and devise a distributed randomized constant-time algorithm for computing strong (O(1), O(n ε))-network-decompositions. As a corollary we derive a constant-time randomized O(n ε)-approximation algorithm for the distributed minimum coloring problem. This improves the best previously-known O(n 1/2 + ε) approximation guarantee. We also derive other improved distributed algorithms for a variety of problems.

Most notably, for the extremely well-studied distributed minimum dominating set problem currently there is no known deterministic polylogarithmic -time algorithm. We devise a deterministic polylogarithmic-time approximation algorithm for this problem, addressing an open problem of Lenzen and Wattenhofer (2010).

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Author information

Authors and Affiliations

  1. Open University of Israel, Ra’anana, Israel

    Leonid Barenboim

  2. Ben-Gurion University of the Negev, Beersheba, Israel

    Michael Elkin

  3. LaBRI - Universite de Bordeaux, Bordeaux, France

    Cyril Gavoille

Authors
  1. Leonid Barenboim
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  2. Michael Elkin
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  3. Cyril Gavoille
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Corresponding author

Correspondence to Leonid Barenboim .

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Editors and Affiliations

  1. Dept of Mathematics and Comp Science, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Christian Scheideler

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Barenboim, L., Elkin, M., Gavoille, C. (2015). A Fast Network-Decomposition Algorithm and Its Applications to Constant-Time Distributed Computation. In: Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2015. Lecture Notes in Computer Science(), vol 9439. Springer, Cham. https://doi.org/10.1007/978-3-319-25258-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-25258-2_15

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