Sublinear bounds for randomized leader election

Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, Amitabh Trehan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations


This paper concerns randomized leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete n-node networks that runs in O(1) rounds and (with high probability) takes only O(√n log3/2 n) messages to elect a unique leader (with high probability). This algorithm is then extended to solve leader election on any connected non-bipartite n-node graph G in O(τ(G)) time and O(τ(G)√n log3/2 n) messages, where τ(G) is the mixing time of a random walk on G. The above result implies highly efficient (sublinear running time and messages) leader election algorithms for networks with small mixing times, such as expanders and hypercubes. In contrast, previous leader election algorithms had at least linear message complexity even in complete graphs. Moreover, super-linear message lower bounds are known for time-efficient deterministic leader election algorithms. Finally, an almost-tight lower bound is presented for randomized leader election, showing that Ω(√n) messages are needed for any O (1) time leader election algorithm which succeeds with high probability. It is also shown that Ω (n1/3 ) messages are needed by any leader election algorithm that succeeds with high probability, regardless of the number of the rounds. We view our results as a step towards understanding the randomized complexity of leader election in distributed networks.

Original languageEnglish (US)
Title of host publicationDistributed Computing and Networking - 14th International Conference, ICDCN 2013, Proceedings
Number of pages15
StatePublished - 2013
Externally publishedYes
Event14th International Conference on Distributed Computing and Networking, ICDCN 2013 - Mumbai, India
Duration: Jan 3 2013Jan 6 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7730 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Conference on Distributed Computing and Networking, ICDCN 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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