Singularly Near Optimal Leader Election in Asynchronous Networks

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

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Author Details

Shay Kutten
  • Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Haifa, Israel
William K. Moses Jr.
  • Department of Computer Science, University of Houston, TX, USA
Gopal Pandurangan
  • Department of Computer Science, University of Houston, TX, USA
David Peleg
  • Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel

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Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg. Singularly Near Optimal Leader Election in Asynchronous Networks. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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. 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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Mathematics of computing → Probabilistic algorithms
  • Mathematics of computing → Discrete mathematics
  • Leader election
  • Singular optimality
  • Randomized algorithms
  • Asynchronous networks
  • Arbitrary graphs


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