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 language | English |
|---|---|
| Title of host publication | 35th International Symposium on Distributed Computing, DISC 2021 |
| Editors | Seth Gilbert |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959772105 |
| DOIs | |
| State | Published - 1 Oct 2021 |
| Externally published | Yes |
| Event | 35th International Symposium on Distributed Computing, DISC 2021 - Virtual, Freiburg, Germany Duration: 4 Oct 2021 → 8 Oct 2021 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 209 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 35th International Symposium on Distributed Computing, DISC 2021 |
|---|---|
| Country/Territory | Germany |
| City | Virtual, Freiburg |
| Period | 4/10/21 → 8/10/21 |
Bibliographical note
Publisher Copyright:© Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg; licensed under Creative Commons License CC-BY 4.0
Funding
Gopal Pandurangan: This work was supported in part by NSF grants CCF-1717075, CCF-1540512, IIS-1633720, and BSF grant 2016419. David Peleg: This work was supported in part by the US-Israel Binational Science Foundation grant 2016732. Funding Shay Kutten: This work was supported in part by the Bi-national Science Foundation (BSF) grant 2016419. William K. Moses Jr.: Part of this work was done while the author was a postdoc at the Technion – Israel Institute of Technology in Israel. This work was supported in part by a Technion fellowship and in part by NSF grants, CCF1540512, IIS-1633720, CCF-1717075, and BSF grant 2016419.
| Funders | Funder number |
|---|---|
| National Science Foundation | CCF-1540512, IIS-1633720, CCF-1717075 |
| Statens Naturvidenskabelige Forskningsrad | |
| United States-Israel Binational Science Foundation | 2016419, 2016732 |
| Technion-Israel Institute of Technology |
Keywords
- Arbitrary graphs
- Asynchronous networks
- Leader election
- Randomized algorithms
- Singular optimality