From Bezout's Identity to Space-Optimal Election in Anonymous Memory Systems

Emmanuel Godard, Damien Imbs, Michel Raynal, Gadi Taubenfeld

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


An anonymous shared memory REG can be seen as an array of atomic registers such that there is no a priori agreement among the processes on the names of the registers. As an example a very same physical register can be known as REG[x] by a process p and as REG[y] (where y ≠ x) by another process q. Moreover, the register known as REG[a] by a process p and the register known as REG[b] by a process q can be the same physical register. It is assumed that each process has a unique identifier that can only be compared for equality. This article is on solving the d-election problem, in which it is required to elect at least one and at most d leaders, in such an anonymous shared memory system. We notice that the 1-election problem is the familiar leader election problem. Let n be the number of processes and m the size of the anonymous memory (number of atomic registers). The article shows that the condition gcd(m, n) ≤ d is necessary and sufficient for solving the d-election problem, where communication is through read/write or read+modify+write registers. The algorithm used to prove the sufficient condition relies on Bezout's Identity - a Diophantine equation relating numbers according to their Greatest Common Divisor. Furthermore, in the process of proving the sufficient condition, it is shown that 1-leader election can be solved using only a single read/write register (which refutes a 1989 conjecture stating that three non-anonymous registers are necessary), and that the exact d-election problem, where exactly d leaders must be elected, can be solved if and only if gcd(m, n) divides d.

Original languageEnglish
Title of host publicationPODC 2020 - Proceedings of the 39th Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Electronic)9781450375825
StatePublished - 31 Jul 2020
Externally publishedYes
Event39th Symposium on Principles of Distributed Computing, PODC 2020 - Virtual, Online, Italy
Duration: 3 Aug 20207 Aug 2020

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference39th Symposium on Principles of Distributed Computing, PODC 2020
CityVirtual, Online

Bibliographical note

Publisher Copyright:
© 2020 ACM.


  • RW register
  • anonymous register
  • asynchrony
  • atomic register
  • bezout identity
  • bounded register
  • concurrent algorithm
  • equality-based comparison
  • leader election
  • process identity
  • symmetric algorithm
  • symmetry breaking


Dive into the research topics of 'From Bezout's Identity to Space-Optimal Election in Anonymous Memory Systems'. Together they form a unique fingerprint.

Cite this