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Planar quorums

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Distributed Algorithms (WDAG 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1151))

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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 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.

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Author information

Authors and Affiliations

  1. School of Computer Science, Florida International University, 33199, Miami, Florida, USA

    Rida A. Bazzi

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  1. Rida A. Bazzi
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Özalp Babaoğlu Keith Marzullo

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© 1996 Springer-Verlag Berlin Heidelberg

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Bazzi, R.A. (1996). Planar quorums. In: Babaoğlu, Ö., Marzullo, K. (eds) Distributed Algorithms. WDAG 1996. Lecture Notes in Computer Science, vol 1151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61769-8_17

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  • DOI: https://doi.org/10.1007/3-540-61769-8_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61769-3

  • Online ISBN: 978-3-540-70679-3

  • eBook Packages: Springer Book Archive

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