The availability of crumbling wall quorum systems

David Peleg; Avishai Wool

doi:10.1016/s0166-218x(96)00016-9

The availability of crumbling wall quorum systems

David Peleg, Avishai Wool

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information. Crumbling walls are a general class of quorum systems. The elements (processors) of a wall are logically arranged in rows of varying widths. A quorum in a wall is the union of one full row and a representative from every row below the full row. This class considerably generalizes a number of known quorum system constructions. In this paper we study the availability of crumbling wall quorum systems. We show that if the row width is bounded, or if the number of rows is bounded, then the wall's failure probability F_p does not vanish as the number of elements tends to infinity (i.e., F_p is not Condorcet). If the wall may grow in both the row number and row width, we show that the behavior depends on the rate of growth of the row width. We establish a sharp threshold rate: when the row width n_i ≤ [log₂ 21] then F_p is Condorcet, and when n_i ≥ (1 + ∈) log₂ i then F_p is not Condorcet.

Original language	English
Pages (from-to)	69-83
Number of pages	15
Journal	Discrete Applied Mathematics
Volume	74
Issue number	1
DOIs	https://doi.org/10.1016/s0166-218x(96)00016-9
State	Published - 4 Apr 1997
Externally published	Yes

Bibliographical note

Funding Information:
” An extended abstract of this work has appeared in the 14’th ACM Symp. Princip. of Dist. Comp., 1995. * Corresponding author. E-mail: [email protected]. ’ Supported in part by a Walter and Elise Haas Career Development Award and by a grant from the Israel Science Foundation. E-mail: [email protected]~mann.ac.il.

Funding

” An extended abstract of this work has appeared in the 14’th ACM Symp. Princip. of Dist. Comp., 1995. * Corresponding author. E-mail: [email protected]. ’ Supported in part by a Walter and Elise Haas Career Development Award and by a grant from the Israel Science Foundation. E-mail: [email protected]~mann.ac.il.

Funders	Funder number
Israel Science Foundation

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10.1016/s0166-218x(96)00016-9

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The availability of crumbling wall quorum systems

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