### Abstract

Quorum systems are 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 failures. 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) |
---|---|

Pages (from-to) | 243-268 |

Number of pages | 26 |

Journal | Theoretical Computer Science |

Volume | 243 |

Issue number | 1-2 |

State | Published - Jul 28 2000 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

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

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Planar quorums

AU - Bazzi, Rida

PY - 2000/7/28

Y1 - 2000/7/28

N2 - Quorum systems are 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 failures. 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 are 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 failures. 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

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UR - http://www.scopus.com/inward/citedby.url?scp=0004352840&partnerID=8YFLogxK

M3 - Article

VL - 243

SP - 243

EP - 268

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -