On the Message Complexity of Fault-Tolerant Computation: Leader Election and Agreement

Manish Kumar, Anisur Rahaman Molla

Research output: Contribution to journalArticlepeer-review


This paper investigates the message complexity of two fundamental problems, leader election and agreement in the crash-fault synchronous and fully-connected distributed network. We present randomized (Monte Carlo) algorithms for both the problems and also show non-trivial lower bounds on the message complexity. Our algorithms achieve sublinear message complexity in the so-called implicit version of the two problems when tolerating more than a constant fraction of the faulty nodes. In comparison to the state-of-art, our results improved and extended the works of [Gilbert-Kowalski, SODA&#x0027;10] (which studied only the agreement problem) in several directions. Specifically, our algorithms tolerate any number of faulty nodes up to <inline-formula><tex-math notation="LaTeX">$(n -\operatorname{polylog}n)$</tex-math></inline-formula>. The message complexity (and also the time complexity) of our algorithms is optimal (up to a <inline-formula><tex-math notation="LaTeX">$\operatorname{polylog}n$</tex-math></inline-formula> factor). Further, our algorithm works in anonymous networks, where nodes do not know each other. To the best of our knowledge, these are the first sub-linear results for both the leader election and the agreement problem in the crash-fault distributed networks.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalIEEE Transactions on Parallel and Distributed Systems
StateAccepted/In press - 1 Jan 2023
Externally publishedYes


  • Agreement
  • Complexity theory
  • Computer crashes
  • Crash-Fault
  • Distributed Algorithm
  • Fault tolerance
  • Fault tolerant systems
  • Fault-Tolerant Algorithm
  • Leader Election
  • Message Complexity
  • Peer-to-peer computing
  • Protocols
  • Randomized Algorithm
  • Voting

ASJC Scopus subject areas

  • Signal Processing
  • Hardware and Architecture
  • Computational Theory and Mathematics


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