Singularly near optimal leader election in asynchronous networks

Shay Kutten, William K. Moses, Gopal Pandurangan, David Peleg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

This paper concerns designing distributed algorithms that are singularly optimal, i.e., algorithms that are simultaneously time and message optimal, for the fundamental leader election problem in asynchronous networks. Kutten et al. (JACM 2015) presented a singularly near optimal randomized leader election algorithm for general synchronous networks that ran in O(D) time and used O(m log n) messages (where D, m, and n are the network’s diameter, number of edges and number of nodes, respectively) with high probability.1 Both bounds are near optimal (up to a logarithmic factor), since Ω(D) and Ω(m) are the respective lower bounds for time and messages for leader election even for synchronous networks and even for (Monte-Carlo) randomized algorithms. On the other hand, for general asynchronous networks, leader election algorithms are only known that are either time or message optimal, but not both. Kutten et al. (DISC 2020) presented a randomized asynchronous leader election algorithm that is singularly near optimal for complete networks, but left open the problem for general networks. This paper shows that singularly near optimal (up to polylogarithmic factors) bounds can be achieved for general asynchronous networks. We present a randomized singularly near optimal leader election algorithm that runs in O(D + log2 n) time and O(m log2 n) messages with high probability. Our result is the first known distributed leader election algorithm for asynchronous networks that is near optimal with respect to both time and message complexity and improves over a long line of results including the classical results of Gallager et al. (ACM TOPLAS, 1983), Peleg (JPDC, 1989), and Awerbuch (STOC, 89).

Original languageEnglish
Title of host publication35th International Symposium on Distributed Computing, DISC 2021
EditorsSeth Gilbert
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772105
DOIs
StatePublished - 1 Oct 2021
Externally publishedYes
Event35th International Symposium on Distributed Computing, DISC 2021 - Virtual, Freiburg, Germany
Duration: 4 Oct 20218 Oct 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume209
ISSN (Print)1868-8969

Conference

Conference35th International Symposium on Distributed Computing, DISC 2021
Country/TerritoryGermany
CityVirtual, Freiburg
Period4/10/218/10/21

Bibliographical note

Publisher Copyright:
© Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg; licensed under Creative Commons License CC-BY 4.0

Keywords

  • Arbitrary graphs
  • Asynchronous networks
  • Leader election
  • Randomized algorithms
  • Singular optimality

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