Singularly optimal randomized leader election

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 networks. Our main result is a randomized distributed leader election algorithm for asynchronous complete networks that is essentially (up to a polylogarithmic factor) singularly optimal. Our algorithm uses O(n) messages with high probability1 and runs in O(log2 n) time (with high probability) to elect a unique leader. The O(n) message complexity should be contrasted with the Ω(n log n) lower bounds for the deterministic message complexity of leader election algorithms (regardless of time), proven by Korach, Moran, and Zaks (TCS, 1989) for asynchronous algorithms and by Afek and Gafni (SIAM J. Comput., 1991) for synchronous networks. Hence, our result also separates the message complexities of randomized and deterministic leader election. More importantly, our (randomized) time complexity of O(log2 n) for obtaining the optimal O(n) message complexity is significantly smaller than the long-standing Θ(∼ n) time complexity obtained by Afek and Gafni and by Singh (SIAM J. Comput., 1997) for message optimal (deterministic) election in asynchronous networks. Afek and Gafni also conjectured that Θ(∼ n) time would be optimal for message-optimal asynchronous algorithms. Our result shows that randomized algorithms are significantly faster. Turning to synchronous complete networks, Afek and Gafni showed an essentially singularly optimal deterministic algorithm with O(log n) time and O(n log n) messages. Ramanathan et al. (Distrib. Comput. 2007) used randomization to improve the message complexity, and showed a randomized algorithm with O(n) messages but still with O(log n) time (with failure probability O(1/ logΩ(1) n)). Our second result shows that synchronous complete networks admit a tightly singularly optimal randomized algorithm, with O(1) time and O(n) messages (both bounds are optimal). Moreover, our algorithm's time bound holds with certainty, and its message bound holds with high probability, i.e., 1 − 1/nc for constant c. Our results demonstrate that leader election can be solved in a simultaneously message and time-efficient manner in asynchronous complete networks using randomization. It is open whether this is possible in asynchronous general networks.

Original languageEnglish
Title of host publication34th International Symposium on Distributed Computing, DISC 2020
EditorsHagit Attiya
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771689
DOIs
StatePublished - 1 Oct 2020
Externally publishedYes
Event34th International Symposium on Distributed Computing, DISC 2020 - Virtual, Online
Duration: 12 Oct 202016 Oct 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume179
ISSN (Print)1868-8969

Conference

Conference34th International Symposium on Distributed Computing, DISC 2020
CityVirtual, Online
Period12/10/2016/10/20

Bibliographical note

Publisher Copyright:
© Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg; licensed under Creative Commons License CC-BY 34th International Symposium on Distributed Computing (DISC 2020).

Funding

Funding Shay Kutten: This work was supported in part by the Bi-national Science Foundation (BSF) grant 2016419. William K. Moses Jr.: This work was supported in part by the BSF grant 2016419 and in part by a Technion fellowship. Gopal Pandurangan: G. Pandurangan was supported, in part, by NSF grants CCF-1527867, CCF-1540512, IIS-1633720, CCF-1717075, and BSF grant 2016419. David Peleg: Supported in part by the US-Israel Binational Science Foundation grant 2016732.

FundersFunder number
National Science FoundationCCF-1527867, CCF-1540512, IIS-1633720, CCF-1717075
Statens Naturvidenskabelige Forskningsrad2016419
United States-Israel Binational Science Foundation2016732
Technion-Israel Institute of Technology

    Keywords

    • Asynchronous systems
    • Complete networks
    • Leader election
    • Randomized algorithms
    • Singularly optimal

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