On the complexity of universal leader election

Shay Kutten, Gopal Pandurangan, David Peleg, Peter Robinson, Amitabh Trehan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Electing a leader is a fundamental task in distributed computing. In its implicit version, only the leader must know who is the elected leader. This paper focuses on studying the message and time complexity of randomized implicit leader election in synchronous distributed networks. Surprisingly, the most \obvious "complexity bounds have not been proven for randomized algorithms. The \obvious" lower bounds of (m) messages (m is the number of edges in the network) and (D) time (D is the network diameter) are non-trivial to show for randomized (Monte Carlo) algorithms. (Recent results that show that even (n) (n is the number of nodes in the network) is not a lower bound on the messages in complete networks, make the above bounds somewhat less obvious). To the best of our knowledge, these basic lower bounds have not been established even for deterministic algorithms (except for the limited case of comparison algorithms, where it was also required that some nodes may not wake up spontaneously, and that D and n were not known). We establish these fundamental lower bounds in this paper for the general case, even for randomized Monte Carlo algorithms. Our lower bounds are universal in the sense that they hold for all universal algorithms (such algorithms should work for all graphs), apply to every D, m, and n, and hold even if D, m, and n are known, all the nodes wake up simultaneously, and the algorithms can make any use of node's identities. To show that these bounds are tight, we present an O(m) messages algorithm. An O(D) time algorithm is known. A slight adaptation of our lower bound technique gives rise to an ω (m) message lower bound for randomized broadcast algorithms. An interesting fundamental problem is whether both upper bounds (messages and time) can be reached simultaneously in the randomized setting for all graphs. (The answer is known to be negative in the deterministic setting). We answer this problem partially by presenting a randomized algorithm that matches both complexities in some cases. This already separates (for some cases) randomized algorithms from deterministic ones. As first steps towards the general case, we present several universal leader election algorithms with bounds that trade-off messages versus time. We view our results as a step towards understanding the complexity of universal leader election in distributed networks.

Original languageEnglish (US)
Title of host publicationPODC 2013 - Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing
Pages100-109
Number of pages10
DOIs
StatePublished - 2013
Externally publishedYes
Event2013 ACM Symposium on Principles of Distributed Computing, PODC 2013 - Montreal, QC, Canada
Duration: Jul 22 2013Jul 24 2013

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing

Conference

Conference2013 ACM Symposium on Principles of Distributed Computing, PODC 2013
Country/TerritoryCanada
CityMontreal, QC
Period7/22/137/24/13

Keywords

  • Distributed algorithm
  • Leader election
  • Lower bound

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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