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Algorithmica

, Volume 81, Issue 5, pp 1901–1920 | Cite as

Deterministic Leader Election Takes \(\Theta (D + \log n)\) Bit Rounds

  • A. CasteigtsEmail author
  • Y. Métivier
  • J. M. Robson
  • A. Zemmari
Article
  • 64 Downloads

Abstract

Leader election is, together with consensus, one of the most central problems in distributed computing. This paper presents a distributed algorithm, called \(\mathcal{STT}\) , for electing deterministically a leader in an arbitrary network, assuming processors have unique identifiers of size \(O(\log n)\), where n is the number of processors. It elects a leader in \(O(D +\log n)\) rounds, where D is the diameter of the network, with messages of size O(1). Thus it has a bit round complexity of \(O(D +\log n)\). This substantially improves upon the best known algorithm whose bit round complexity is \(O(D\log n)\). In fact, using the lower bound by Kutten et al. (J ACM 62(1):7:1–7:27, 2015) and Kutten et al. (Theor Comput Sci 561:134–143, 2015) and a result of Dinitz and Solomon (Theor Comput Sci 384(2–3):168–183, 2007), we show that the bit round complexity of \(\mathcal{STT}\) is optimal (up to a constant factor), which is a significant step forward in understanding the interplay between time and message optimality for the election problem. Our algorithm requires no knowledge on the graph such as n or D, and the pipelining technique we introduce to break the \(O(D\log n)\) barrier is general.

Notes

Acknowledgements

We thank the anonymous referees for their many helpful comments on an earlier version of this article.

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Authors and Affiliations

  1. 1.Université de Bordeaux - Bordeaux INP LaBRI, UMR CNRS 5800TalenceFrance

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