Billiard quorums on the grid

Divyakant Agrawal, Ömer Eǧecioǧlu, Amr El Abbadi

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Maekawa considered a simple but suboptimal grid based quorum generation scheme in which N sites in a network are logically organized in the form of a √N × √N grid, and the quorum sets are row-column pairs. Even though the quorum size 2√N of the grid scheme is twice as large as finite projective plane based optimal size quorums, it has the advantage of being simple and geometrically evident. In this paper we construct grid based quorums which use a modified grid, and paths that resemble billiard ball paths instead of horizontal and vertical line segments of rows and columns in the grid scheme. The size of these quorums is √2√N. The construction and its properties are geometrically evident as in the case of Maekawa's grid, and the quorum sets can be generated efficiently.

Original languageEnglish
Pages (from-to)9-16
Number of pages8
JournalInformation Processing Letters
Volume64
Issue number1
Publication statusPublished - 14 Oct 1997
Externally publishedYes

Fingerprint

Quorum
Billiards
Grid
Finite projective plane
Path
Line segment
Ball
Horizontal
Vertical

Keywords

  • Coterie
  • Distributed system
  • Mutual exclusion
  • Quorum

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Agrawal, D., Eǧecioǧlu, Ö., & El Abbadi, A. (1997). Billiard quorums on the grid. Information Processing Letters, 64(1), 9-16.

Billiard quorums on the grid. / Agrawal, Divyakant; Eǧecioǧlu, Ömer; El Abbadi, Amr.

In: Information Processing Letters, Vol. 64, No. 1, 14.10.1997, p. 9-16.

Research output: Contribution to journalArticle

Agrawal, D, Eǧecioǧlu, Ö & El Abbadi, A 1997, 'Billiard quorums on the grid', Information Processing Letters, vol. 64, no. 1, pp. 9-16.
Agrawal D, Eǧecioǧlu Ö, El Abbadi A. Billiard quorums on the grid. Information Processing Letters. 1997 Oct 14;64(1):9-16.
Agrawal, Divyakant ; Eǧecioǧlu, Ömer ; El Abbadi, Amr. / Billiard quorums on the grid. In: Information Processing Letters. 1997 ; Vol. 64, No. 1. pp. 9-16.
@article{f06401198173485dbb38722adc8f1d2f,
title = "Billiard quorums on the grid",
abstract = "Maekawa considered a simple but suboptimal grid based quorum generation scheme in which N sites in a network are logically organized in the form of a √N × √N grid, and the quorum sets are row-column pairs. Even though the quorum size 2√N of the grid scheme is twice as large as finite projective plane based optimal size quorums, it has the advantage of being simple and geometrically evident. In this paper we construct grid based quorums which use a modified grid, and paths that resemble billiard ball paths instead of horizontal and vertical line segments of rows and columns in the grid scheme. The size of these quorums is √2√N. The construction and its properties are geometrically evident as in the case of Maekawa's grid, and the quorum sets can be generated efficiently.",
keywords = "Coterie, Distributed system, Mutual exclusion, Quorum",
author = "Divyakant Agrawal and {\"O}mer Eǧecioǧlu and {El Abbadi}, Amr",
year = "1997",
month = "10",
day = "14",
language = "English",
volume = "64",
pages = "9--16",
journal = "Information Processing Letters",
issn = "0020-0190",
publisher = "Elsevier",
number = "1",

}

TY - JOUR

T1 - Billiard quorums on the grid

AU - Agrawal, Divyakant

AU - Eǧecioǧlu, Ömer

AU - El Abbadi, Amr

PY - 1997/10/14

Y1 - 1997/10/14

N2 - Maekawa considered a simple but suboptimal grid based quorum generation scheme in which N sites in a network are logically organized in the form of a √N × √N grid, and the quorum sets are row-column pairs. Even though the quorum size 2√N of the grid scheme is twice as large as finite projective plane based optimal size quorums, it has the advantage of being simple and geometrically evident. In this paper we construct grid based quorums which use a modified grid, and paths that resemble billiard ball paths instead of horizontal and vertical line segments of rows and columns in the grid scheme. The size of these quorums is √2√N. The construction and its properties are geometrically evident as in the case of Maekawa's grid, and the quorum sets can be generated efficiently.

AB - Maekawa considered a simple but suboptimal grid based quorum generation scheme in which N sites in a network are logically organized in the form of a √N × √N grid, and the quorum sets are row-column pairs. Even though the quorum size 2√N of the grid scheme is twice as large as finite projective plane based optimal size quorums, it has the advantage of being simple and geometrically evident. In this paper we construct grid based quorums which use a modified grid, and paths that resemble billiard ball paths instead of horizontal and vertical line segments of rows and columns in the grid scheme. The size of these quorums is √2√N. The construction and its properties are geometrically evident as in the case of Maekawa's grid, and the quorum sets can be generated efficiently.

KW - Coterie

KW - Distributed system

KW - Mutual exclusion

KW - Quorum

UR - http://www.scopus.com/inward/record.url?scp=0001965487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001965487&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001965487

VL - 64

SP - 9

EP - 16

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 1

ER -