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

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Bordeaux, LaBRI, UMR 5800TalenceFrance
  2. 2.CNRS, LaBRI, UMR 5800TalenceFrance

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