Quorum systems constructed from combinatorial designs

Charles Colbourn, Jeffrey H. Dinitz, Douglas R. Stinson

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A quorum system is a set system in which any two subsets have nonempty intersection. Quorum systems have been extensively studied as a method of maintaining consistency in distributed systems. Important attributes of a quorum system include the load, balancing ratio, rank (i.e., quorum size), and availability. Many constructions have been presented in the literature for quorum systems in which these attributes take on optimal or otherwise favorable values. In this paper, we point out an elementary connection between quorum systems and the classical covering systems studied in combinatorial design theory. We look more closely at the quorum systems that are obtained from balanced incomplete block designs (BIBDs). We study the properties of these quorum systems and observe that they have load, balancing ratio, and rank that are all within a constant factor of being optimal. We also provide several observations about computing the failure polynomials of a quorum system (failure polynomials are used to measure availability). Asymptotic properties of failure polynomials have previously been analyzed for certain infinite families of quorum systems. We give an explicit formula for the failure polynomials for an easily constructed infinite class of quorum systems. We also develop two algorithms that are useful for computing failure polynomials for quorum systems and prove that computing failure polynomials is #P-hard. Computational results are presented for several "small" quorum systems obtained from BIBDs.

Original languageEnglish (US)
Pages (from-to)160-173
Number of pages14
JournalInformation and Computation
Volume169
Issue number2
DOIs
StatePublished - Sep 15 2001
Externally publishedYes

Fingerprint

Quorum
Combinatorial Design
Polynomials
Resource allocation
Polynomial
Availability
Balanced Incomplete Block Design
Load Balancing
Computing
Attribute
Covering Systems
Set Systems
Asymptotic Properties
Computational Results

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Quorum systems constructed from combinatorial designs. / Colbourn, Charles; Dinitz, Jeffrey H.; Stinson, Douglas R.

In: Information and Computation, Vol. 169, No. 2, 15.09.2001, p. 160-173.

Research output: Contribution to journalArticle

Colbourn, Charles ; Dinitz, Jeffrey H. ; Stinson, Douglas R. / Quorum systems constructed from combinatorial designs. In: Information and Computation. 2001 ; Vol. 169, No. 2. pp. 160-173.
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