Document Open Access Logo

Singularly Near Optimal Leader Election in Asynchronous Networks

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

PDF
Thumbnail PDF

File

LIPIcs.DISC.2021.27.pdf
  • Filesize: 0.95 MB
  • 18 pages

Document Identifiers

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

Funding

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

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.DISC.2021.27

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Yehuda Afek and Eli Gafni. Time and message bounds for election in synchronous and asynchronous complete networks. SICOMP, 20(2):376-394, 1991. Google Scholar
  2. Yehuda Afek and Yossi Matias. Elections in anonymous networks. Information and Computation, 113(2):312-330, 1994. Google Scholar
  3. Dana Angluin. Local and global properties in networks of processors (extended abstract). In STOC, pages 82-93, 1980. URL: https://doi.org/10.1145/800141.804655.
  4. Baruch Awerbuch. Complexity of network synchronization. Journal of the ACM (JACM), 32(4):804-823, 1985. Google Scholar
  5. Baruch Awerbuch. Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems. In Proceedings of the 19th ACM Symposium on Theory of Computing (STOC), pages 230-240, 1987. Google Scholar
  6. Baruch Awerbuch. Distributed shortest paths algorithms (extended abstract). In Proceedings of the twenty-first annual ACM symposium on Theory of computing, pages 490-500, 1989. Google Scholar
  7. Baruch Awerbuch and Robert G Gallager. Distributed bfs algorithms. In 26th Annual Symposium on Foundations of Computer Science (sfcs 1985), pages 250-256. IEEE, 1985. Google Scholar
  8. Baruch Awerbuch, Oded Goldreich, David Peleg, and Ronen Vainish. A trade-off between information and communication in broadcast protocols. J. ACM, 37(2):238-256, 1990. Google Scholar
  9. Baruch Awerbuch and David Peleg. Network synchronization with polylogarithmic overhead. In Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, pages 514-522. IEEE, 1990. Google Scholar
  10. Tushar D. Chandra, Robert Griesemer, and Joshua Redstone. Paxos made live: an engineering perspective. In Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing, pages 398-407, 2007. Google Scholar
  11. Fay Chang, Jeffrey Dean, Sanjay Ghemawat, Wilson C Hsieh, Deborah A Wallach, Mike Burrows, Tushar Chandra, Andrew Fikes, and Robert E Gruber. Bigtable: A distributed storage system for structured data. ACM Transactions on Computer Systems (TOCS), 26(2):1-26, 2008. Google Scholar
  12. Soumyottam Chatterjee, Gopal Pandurangan, and Peter Robinson. The complexity of leader election in diameter-two networks. Distributed Computing, pages 1-17, 2019. Google Scholar
  13. F. Chin and H. F. Ting. Improving the time complexity of message-optimal distributed algorithms for minimum-weight spanning trees. SIAM Journal on Computing, 19(4):612-626, 1990. Google Scholar
  14. Michael Elkin. A simple deterministic distributed mst algorithm, with near-optimal time and message complexities. In PODC, pages 157-163, 2017. Google Scholar
  15. Michalis Faloutsos and Mart Molle. A linear-time optimal-message distributed algorithm for minimum spanning trees. Distributed Computing, 17(2):151-170, 2004. Google Scholar
  16. Eli Gafni. Improvements in the time complexity of two message-optimal election algorithms. In Proceedings of the 4th Symposium on Principles of Distributed Computing (PODC), pages 175-185, 1985. Google Scholar
  17. Robert G. Gallager, Pierre A. Humblet, and Philip M. Spira. A distributed algorithm for minimum-weight spanning trees. ACM Trans. Programming Languages & systems (TOPLAS), 5(1):66-77, January 1983. URL: https://doi.org/10.1145/357195.357200.
  18. Mohsen Ghaffari and Fabian Kuhn. Distributed MST and broadcast with fewer messages, and faster gossiping. In Proceedings of the 32nd International Symposium on Distributed Computing (DISC), pages 30:1-30:12, 2018. Google Scholar
  19. Sanjay Ghemawat, Howard Gobioff, and Shun-Tak Leung. The google file system. In Proceedings of the nineteenth ACM symposium on Operating systems principles, pages 29-43, 2003. Google Scholar
  20. Seth Gilbert, Peter Robinson, and Suman Sourav. Leader election in well-connected graphs. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, pages 227-236, 2018. Google Scholar
  21. Robert Gmyr and Gopal Pandurangan. Time-message trade-offs in distributed algorithms. In 32nd International Symposium on Distributed Computing, DISC 2018, New Orleans, LA, USA, October 15-19, 2018, pages 32:1-32:18, 2018. Google Scholar
  22. Bernhard Haeupler, D. Ellis Hershkowitz, and David Wajc. Round-and message-optimal distributed graph algorithms. In PODC, pages 119-128, 2018. Google Scholar
  23. Pierre A. Humblet. Selecting a leader in a clique in O(n log n) messages. Memo, Lab. for Information & Decision Systems, MIT, 1984. Google Scholar
  24. Alon Itai and Michael Rodeh. Symmetry breaking in distributed networks. Inf. Comput., 88(1):60-87, 1990. Google Scholar
  25. Maleq Khan, Fabian Kuhn, Dahlia Malkhi, Gopal Pandurangan, and Kunal Talwar. Efficient distributed approximation algorithms via probabilistic tree embeddings. In Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing, PODC '08, pages 263-272, New York, NY, USA, 2008. ACM. URL: https://doi.org/10.1145/1400751.1400787.
  26. Valerie King, Shay Kutten, and Mikkel Thorup. Construction and impromptu repair of an MST in a distributed network with o(m) communication. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC), pages 71-80, 2015. Google Scholar
  27. Ephraim Korach, Shay Kutten, and Shlomo Moran. A modular technique for the design of efficient distributed leader finding algorithms. ACM Trans. Programming Languages & Systems (TOPLAS), 12(1):84-101, 1990. URL: https://doi.org/10.1145/77606.77610.
  28. Ephraim Korach, Shlomo Moran, and Shmuel Zaks. Tight lower and upper bounds for some distributed algorithms for a complete network of processors. In Proceedings of the third annual ACM symposium on Principles of distributed computing, pages 199-207, New York, NY, USA, 1984. ACM. URL: https://doi.org/10.1145/800222.806747.
  29. Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg. Singularly optimal randomized leader election. In Hagit Attiya, editor, 34th International Symposium on Distributed Computing, DISC 2020, October 12-16, 2020, Virtual Conference, volume 179 of LIPIcs, pages 22:1-22:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.DISC.2020.22.
  30. Shay Kutten, William K. Moses Jr., Gopal Pandurangan, and David Peleg. Singularly near optimal leader election in asynchronous networks. CoRR, abs/2108.02197, 2021. URL: http://arxiv.org/abs/2108.02197.
  31. Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. On the complexity of universal leader election. J. ACM, 62:7, 2015. Google Scholar
  32. Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, and Amitabh Trehan. Sublinear bounds for randomized leader election. Theoretical Computer Science, 561:134-143, 2015. Google Scholar
  33. Gérard Le Lann. Distributed systems - towards a formal approach. In IFIP Congress, pages 155-160, 1977. Google Scholar
  34. Ivan Lavallée and Christian Lavault. Spanning tree construction for nameless networks. In International Workshop on Distributed Algorithms, pages 41-56. Springer, 1990. Google Scholar
  35. Nancy Lynch. Distributed Algorithms. Morgan Kaufman Publishers, Inc., San Francisco, USA, 1996. Google Scholar
  36. Ali Mashreghi and Valerie King. Time-communication trade-offs for minimum spanning tree construction. In Proceedings of the 18th International Conference on Distributed Computing and Networking (ICDCN), 2017. Google Scholar
  37. Ali Mashreghi and Valerie King. Brief announcement: Faster asynchronous MST and low diameter tree construction with sublinear communication. In Jukka Suomela, editor, 33rd International Symposium on Distributed Computing, DISC 2019, October 14-18, 2019, Budapest, Hungary, volume 146 of LIPIcs, pages 49:1-49:3, 2019. Google Scholar
  38. Ali Mashreghi and Valerie King. Broadcast and minimum spanning tree with o(m) messages in the asynchronous CONGEST model. Distributed Computing, pages 1-17, 2021. Google Scholar
  39. Michael Mitzenmacher and Eli Upfal. Probability and computing: randomization and probabilistic techniques in algorithms and data analysis. Cambridge university press, 2017. Google Scholar
  40. Gopal Pandurangan, Peter Robinson, and Michele Scquizzato. A time- and message-optimal distributed algorithm for minimum spanning trees. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, June 19-23, 2017, pages 743-756, 2017. Google Scholar
  41. David Peleg. Time-optimal leader election in general networks. J. Parallel & Distributed Computing, 8(1):96-99, 1990. Google Scholar
  42. David Peleg. Distributed Computing: A Locality-Sensitive Approach. Society for Industrial and Applied Mathematics, 2000. Google Scholar
  43. David Peleg and Vitaly Rubinovich. A near-tight lower bound on the time complexity of distributed mst construction. In 40th Annual Symposium on Foundations of Computer Science (Cat. No. 99CB37039), pages 253-261. IEEE, 1999. Google Scholar
  44. Gary Peterson. Efficient algorithms for elections in meshes and complete graphs. Technical report, TR 140, Dept. of CS, Univ. Rochester, 1985. Google Scholar
  45. Murali Krishna Ramanathan, Ronaldo A. Ferreira, Suresh Jagannathan, Ananth Grama, and Wojciech Szpankowski. Randomized leader election. Distributed Computing, pages 403-418, 2007. Google Scholar
  46. Nicola Santoro. Design and Analysis of Distributed Algorithms (Wiley Series on Parallel and Distributed Computing). Wiley-Interscience, 2006. Google Scholar
  47. Baruch Schieber and Marc Snir. Calling names on nameless networks. Information and Computation, 113(1):80-101, 1994. Google Scholar
  48. Gurdip Singh. Efficient leader election using sense of direction. Distributed Computing, 10(3):159-165, 1997. URL: https://doi.org/10.1007/s004460050033.
  49. Gerard Tel. Introduction to distributed algorithms. Cambridge University Press, New York, NY, USA, 1994. Google Scholar
  50. Donald M. Topkis. Performance analysis of information dissemination by flooding. IEEE journal on selected areas in communications, 7(3):335-340, 1989. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact