Sublinear bounds for randomized leader election

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

Research output: Contribution to journalArticlepeer-review

26 Scopus citations

Abstract

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) uses only O(√ √nlog3/2n) messages to elect a unique leader (with high probability). When considering the "explicit" variant of leader election where eventually every node knows the identity of the leader, our algorithm yields the asymptotically optimal bounds of O(1) rounds and O(. n) messages. This algorithm is then extended to one solving leader election on any connected non-bipartite n-node graph G in O(τ(. G)) time and O(τ(G)n√log3/2n) 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, we present an almost matching lower bound for randomized leader election, showing that Ω(n) messages are needed for any leader election algorithm that succeeds with probability at least 1/. e+. ε, for any small constant ε. >. 0. We view our results as a step towards understanding the randomized complexity of leader election in distributed networks.

Original languageEnglish (US)
Pages (from-to)134-143
Number of pages10
JournalTheoretical Computer Science
Volume561
Issue numberPB
DOIs
StatePublished - 2015
Externally publishedYes

Keywords

  • Distributed algorithm
  • Leader election
  • Lower bound
  • Randomization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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