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An Almost-Logarithmic Lower Bound for Leader Election with Bounded Value Contention

Authors Dan Alistarh , Faith Ellen , Alexander Fedorov

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Subject Classification

ACM Subject Classification
  • Theory of computation → Shared memory algorithms
  • Theory of computation → Lower bounds and information complexity
  • Theory of computation → Concurrency
Keywords
  • Leader Election
  • Test-and-Set
  • Shared Memory
  • Lower Bounds

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Abstract

We investigate the step complexity of the Leader Election problem (and implementing the corresponding test-and-set object) in asynchronous shared memory, where processes communicate through registers supporting atomic read and write and must coordinate so that a single process becomes the leader. Determining tight step complexity bounds for solving this problem is one of the key open problems in the theory of shared memory distributed computing. The best known algorithm is a randomized tournament-tree, which has worst-case expected step complexity O(log N) for N processes. There are provably no deterministic wait-free algorithms, and only restricted lower bounds are known for obstruction-free and randomized wait-free algorithms. We introduce a new lower bound that establishes an Ω((log N)/(log log N + log Q)) step complexity for any obstruction-free Leader Election algorithm, where N is the number of processes, and 2 ≤ Q ≤ N is a bound on the value contention, which we define as the maximum number of different values that processes can be simultaneously poised to write to the same register in any execution of the algorithm. Our result is strictly stronger than previous bounds based on write contention. In particular, it implies new lower bounds on step complexity that depend on register size.

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Dan Alistarh, Faith Ellen, and Alexander Fedorov. An Almost-Logarithmic Lower Bound for Leader Election with Bounded Value Contention. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.3

Author Details

Dan Alistarh
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria
Faith Ellen
  • University of Toronto, Canada
Alexander Fedorov
  • Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria

Funding

The work of Dan Alistarh is supported by grants from ERC, Austrian FWF, and the Google and NVIDIA corporations. Faith Ellen was supported in part by the Natural Science and Engineering Research Council of Canada (NSERC) grant RGPIN-2020-04178.

Acknowledgements

The authors would like to thank the DISC 2025 anonymous reviewers for their detailed comments and, in particular, Reviewer C, who inspired our approach for a new and simpler proof of Theorem 5 via the probabilistic method.

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