Self-stabilizing Metric Graphs

  • Robert GmyrEmail author
  • Jonas Lefèvre
  • Christian Scheideler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10083)


We present a self-stabilizing algorithm for overlay networks that, for an arbitrary metric given by 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 stablizes in time O(n) and it is almost silent in that after stabilization a node sends and receives a constant number of messages per round.


Overlay network Self-stabilizing algorithms Metric graph 



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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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Robert Gmyr
    • 1
    Email author
  • Jonas Lefèvre
    • 1
    • 2
  • Christian Scheideler
    • 1
  1. 1.Department of Computer SciencePaderborn UniversityPaderbornGermany
  2. 2.IRIF, University Paris-Diderot – Paris 7ParisFrance

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