Beeping a Deterministic Time-Optimal Leader Election

Authors Fabien Dufoulon , Janna Burman, Joffroy Beauquier

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Author Details

Fabien Dufoulon
  • LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
Janna Burman
  • LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France
Joffroy Beauquier
  • LRI, Université Paris-Sud, CNRS, Université Paris-Saclay, Orsay, France

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Fabien Dufoulon, Janna Burman, and Joffroy Beauquier. Beeping a Deterministic Time-Optimal Leader Election. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we solve the leader election problem with an asymptotically optimal round complexity of O(D + log n), for a network of unknown size n and unknown diameter D (but with unique identifiers). Contrary to the best previously known algorithms in the same setting, the proposed one is deterministic. The techniques we introduce give a new insight as to how local constraints on the exchangeable messages can result in efficient algorithms, when dealing with the beeping model. Using this deterministic leader election algorithm, we obtain a randomized leader election algorithm for anonymous networks with an asymptotically optimal round complexity of O(D + log n) w.h.p. In previous works this complexity was obtained in expectation only. Moreover, using deterministic leader election, we obtain efficient algorithms for symmetry-breaking and communication procedures: O(log n) time MIS and 5-coloring for tree networks (which is time-optimal), as well as k-source multi-broadcast for general graphs in O(min(k,log n) * D + k log{(n M)/k}) rounds (for messages in {1,..., M}). This latter result improves on previous solutions when the number of sources k is sublogarithmic (k = o(log n)).

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Distributed algorithms
  • Theory of computation → Design and analysis of algorithms
  • distributed algorithms
  • leader election
  • beeping model
  • time complexity
  • deterministic algorithms
  • wireless networks


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