Planar quorums

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Quorum systems are used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. This paper presents a new class of quorum systems based on connected regions in planar graphs. This class has an intuitive geometric nature and is easy to visualize and map to the system topology. We show that for triangulated graphs, the resulting quorum systems are non-dominated, which is a desirable property. We study the performance of these systems in terms of their availability, load, and cost of failures. We formally introduce the concept of cost of failures and argue that it is needed to analyze the message complexity of quorum-based protocols. We show that quorums of triangulated graphs with bounded degree have optimal cost of failures. We study a particular member of this class, the triangle lattice. The triangle lattice has small quorum size, optimal load for its size, high availability, and optimal cost of failures. Its parameters are not matched by any other proposed system in the literature. We use percolation theory to study the availability of this system.

Original languageEnglish (US)
Pages (from-to)243-268
Number of pages26
JournalTheoretical Computer Science
Issue number1-2
StatePublished - Jul 28 2000


  • Cost of failures
  • Distributed systems
  • Fault tolerance
  • Load
  • Percolation
  • Planar graphs
  • Quorum systems

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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