### Abstract

Quorum systems Eire used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. This paper presents a new class of quorum systems based on connected regions in planar graphs. This class has an intuitive geometric nature and is easy to visualize and map to the system topology. We show that for triangulated graphs, the resulting quorum systems are non-dominated, which is a desirable property. We study the performance of these systems in terms of their availability, load, and cost of failures. We formally introduce the concept of cost of failures and argue that it is needed to analyze the message complexity of quorum-based protocols. We show that quorums of triangulated graphs with bounded degree have optimal cost of failure. We study a particular member of this class, the triangle lattice. The triangle lattice has small quorum size, optimal load for its size, high availability, and optimal cost of failures. Its parameters are not matched by any other proposed system in the literature. We use percolation theory to study the availability of this system.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 251-268 |

Number of pages | 18 |

Volume | 1151 |

ISBN (Print) | 9783540617693 |

State | Published - 1996 |

Externally published | Yes |

Event | 10th International Workshop on Distributed Algorithms, WDAG 1996 - Bologna, Italy Duration: Oct 9 1996 → Oct 11 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 1151 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th International Workshop on Distributed Algorithms, WDAG 1996 |
---|---|

Country | Italy |

City | Bologna |

Period | 10/9/96 → 10/11/96 |

### Fingerprint

### Keywords

- Cost of failures
- Distributed systems
- Fault tolerance
- Load
- Percolation
- Planar graphs
- Quorum systems

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 1151, pp. 251-268). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1151). Springer Verlag.

**Planar quorums.** / Bazzi, Rida.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 1151, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1151, Springer Verlag, pp. 251-268, 10th International Workshop on Distributed Algorithms, WDAG 1996, Bologna, Italy, 10/9/96.

}

TY - GEN

T1 - Planar quorums

AU - Bazzi, Rida

PY - 1996

Y1 - 1996

N2 - Quorum systems Eire used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. This paper presents a new class of quorum systems based on connected regions in planar graphs. This class has an intuitive geometric nature and is easy to visualize and map to the system topology. We show that for triangulated graphs, the resulting quorum systems are non-dominated, which is a desirable property. We study the performance of these systems in terms of their availability, load, and cost of failures. We formally introduce the concept of cost of failures and argue that it is needed to analyze the message complexity of quorum-based protocols. We show that quorums of triangulated graphs with bounded degree have optimal cost of failure. We study a particular member of this class, the triangle lattice. The triangle lattice has small quorum size, optimal load for its size, high availability, and optimal cost of failures. Its parameters are not matched by any other proposed system in the literature. We use percolation theory to study the availability of this system.

AB - Quorum systems Eire used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. This paper presents a new class of quorum systems based on connected regions in planar graphs. This class has an intuitive geometric nature and is easy to visualize and map to the system topology. We show that for triangulated graphs, the resulting quorum systems are non-dominated, which is a desirable property. We study the performance of these systems in terms of their availability, load, and cost of failures. We formally introduce the concept of cost of failures and argue that it is needed to analyze the message complexity of quorum-based protocols. We show that quorums of triangulated graphs with bounded degree have optimal cost of failure. We study a particular member of this class, the triangle lattice. The triangle lattice has small quorum size, optimal load for its size, high availability, and optimal cost of failures. Its parameters are not matched by any other proposed system in the literature. We use percolation theory to study the availability of this system.

KW - Cost of failures

KW - Distributed systems

KW - Fault tolerance

KW - Load

KW - Percolation

KW - Planar graphs

KW - Quorum systems

UR - http://www.scopus.com/inward/record.url?scp=84955586426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955586426&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540617693

VL - 1151

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 251

EP - 268

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -