Leader election in well-connected graphs

Seth Gilbert, Peter Robinson, Suman Sourav

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

5 Scopus citations

Abstract

In this paper, we look at the problem of randomized leader election in synchronous distributed networks with a special focus on the message complexity. We provide an algorithm that solves the implicit version of leader election (where non-leader nodes need not be aware of the identity of the leader) in any general network with O(n log7/2 n · tmix ) messages and in O(tmix log2 n) time, where n is the number of nodes and tmix refers to the mixing time of a random walk in the network graph G. For several classes of well-connected networks (that have a large conductance or alternatively small mixing times e.g. expanders, hypercubes, etc), the above result implies extremely efficient (sublinear running time and messages) leader election algorithms. Correspondingly, we show that any substantial improvement is not possible over our algorithm, by presenting an almost matching lower bound for randomized leader election. We show that Ω(n/3/4) messages are needed for any leader election algorithm that succeeds with probability at least 1 − o(1), where refers to the conductance of a graph. To the best of our knowledge, this is the first work that shows a dependence between the time and message complexity to solve leader election and the connectivity of the graph G, which is often characterized by the graph's conductance . Apart from the Ω(m) bound in [23] (where m denotes the number of edges of the graph), this work also provides one of the first non-trivial lower bounds for leader election in general networks.

Original languageEnglish (US)
Title of host publicationPODC 2018 - Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Pages227-236
Number of pages10
ISBN (Print)9781450357951
DOIs
StatePublished - Jul 23 2018
Externally publishedYes
Event37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018 - Egham, United Kingdom
Duration: Jul 23 2018Jul 27 2018

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference37th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2018
Country/TerritoryUnited Kingdom
CityEgham
Period7/23/187/27/18

Keywords

  • Conductance
  • Leader election
  • Mixing time
  • Random walks

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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