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A Fully Asynchronous and Fault Tolerant Distributed Algorithm to Compute a Minimum Graph Orientation

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Stabilization, Safety, and Security of Distributed Systems (SSS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10616))

Abstract

The minimum orientation problem is a classical graph theoretical problem in which we aim at finding an orientation of a graph G that minimizes the maximum out-degree \(D^+(G)\). Graph orientation is motivated by load balancing problems in which a set of tasks have to be allocated to a set of processes in order to minimize the completion time. If we consider load balancing in networks, the decisions for the allocation have to be made by the nodes without a global knowledge of the graph. In this paper, we propose a distributed algorithm that computes a graph orientation that provides a \(2(2+\epsilon )\)-approximation of the optimal. The algorithm is asynchronous and runs in \(O((\log n +diam(G))\log D^+(OPT(G))\) rounds, where n is the number of nodes, diam is the diameter of the graph and \(D^+(OPT(G))\) is the maximum out-degree with an optimal orientation. The algorithm does not need any global knowledge on G and tolerates initial faults.

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Notes

  1. 1.

    This result was initially stated for undirected graph but it is immediately adaptable for bi-directed graphs since the both are equivalent representations.

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Author information

Authors and Affiliations

  1. University of Bordeaux, LaBRI, UMR 5800, 33400, Talence, France

    Noël Gillet

  2. CNRS, LaBRI, UMR 5800, 33400, Talence, France

    Nicolas Hanusse

Authors
  1. Noël Gillet
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  2. Nicolas Hanusse
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Correspondence to Noël Gillet .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Paul Spirakis

  2. Chalmers University of Technology, Gothenburg, Sweden

    Philippas Tsigas

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Gillet, N., Hanusse, N. (2017). A Fully Asynchronous and Fault Tolerant Distributed Algorithm to Compute a Minimum Graph Orientation. In: Spirakis, P., Tsigas, P. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2017. Lecture Notes in Computer Science(), vol 10616. Springer, Cham. https://doi.org/10.1007/978-3-319-69084-1_22

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  • DOI: https://doi.org/10.1007/978-3-319-69084-1_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69083-4

  • Online ISBN: 978-3-319-69084-1

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