### 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 language | English |
---|---|

Pages (from-to) | 9-16 |

Number of pages | 8 |

Journal | Information Processing Letters |

Volume | 64 |

Issue number | 1 |

Publication status | Published - 14 Oct 1997 |

Externally published | Yes |

### Fingerprint

### Keywords

- Coterie
- Distributed system
- Mutual exclusion
- Quorum

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Information Processing Letters*,

*64*(1), 9-16.

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

Research output: Contribution to journal › Article

*Information Processing Letters*, vol. 64, no. 1, pp. 9-16.

}

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

VL - 64

SP - 9

EP - 16

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 1

ER -