### 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 language | English (US) |
---|---|

Pages (from-to) | 160-173 |

Number of pages | 14 |

Journal | Information and Computation |

Volume | 169 |

Issue number | 2 |

DOIs | |

State | Published - Sep 15 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Information and Computation*,

*169*(2), 160-173. https://doi.org/10.1006/inco.2001.3044

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

Research output: Contribution to journal › Article

*Information and Computation*, vol. 169, no. 2, pp. 160-173. https://doi.org/10.1006/inco.2001.3044

}

TY - JOUR

T1 - Quorum systems constructed from combinatorial designs

AU - Colbourn, Charles

AU - Dinitz, Jeffrey H.

AU - Stinson, Douglas R.

PY - 2001/9/15

Y1 - 2001/9/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035885987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035885987&partnerID=8YFLogxK

U2 - 10.1006/inco.2001.3044

DO - 10.1006/inco.2001.3044

M3 - Article

AN - SCOPUS:0035885987

VL - 169

SP - 160

EP - 173

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

IS - 2

ER -