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Self-Stabilizing Metric Graphs

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Abstract

We present a self-stabilizing algorithm for overlay networks that for an arbitrary given metric specified via a distance oracle constructs the graph representing that metric. The graph representing a metric is the unique minimal undirected graph such that for any pair of nodes the length of a shortest path between the nodes corresponds to the distance between the nodes according to the metric. The algorithm works under both an asynchronous and a synchronous dæmon. In the synchronous case, the algorithm stabilizes in time O(n), and after stabilization each node sends and receives only a constant number of messages per round.

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Acknowledgements

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901) and by the EU within FET project MULTIPLEX under contract no. 317532.

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Authors and Affiliations

  1. Department of Computer Science, Paderborn University, Paderborn, Germany

    Robert Gmyr, Jonas Lefèvre & Christian Scheideler

  2. IRIf, University Paris-Diderot, Paris 7, Paris, France

    Jonas Lefèvre

Authors
  1. Robert Gmyr
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  2. Jonas Lefèvre
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  3. Christian Scheideler
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Correspondence to Robert Gmyr.

Additional information

This article is part of the Topical Collection on Special Issue on Stabilization, Safety, and Security of Distributed Systems (SSS 2016)

A preliminary version of this work has been presented at the 18th International Symposium on Stabilization, Safety, and Security of Distributed Systems, see [6]. In this extended version, we present the full algorithm including the rules for constructing a sorted ring and we provide proofs for all parts of the algorithm.

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Gmyr, R., Lefèvre, J. & Scheideler, C. Self-Stabilizing Metric Graphs. Theory Comput Syst 63, 177–199 (2019). https://doi.org/10.1007/s00224-017-9823-4

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  • DOI: https://doi.org/10.1007/s00224-017-9823-4

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