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Geographic Quorum System Approximations

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Abstract

Quorum systems are a mechanism for obtaining fault-tolerance and efficient distributed systems. We consider geographic quorum systems; a geographic quorum system is a partition of a set X of sites in the plane (representing servers) into quorums (i.e., clusters) of size k. The distance between a point p and a cluster C is the Euclidean distance between p and the site in C that is the farthest from p. We present a near linear time constant-factor approximation algorithm for partitioning X into clusters, such that the maximal distance between a point in the underlying region and its closest cluster is minimized. Next, we describe a data structure for answering (approximately) nearest-neighbor queries on such a clustering. Finally, we study the problem of partitioning into clusters with an additional load-balancing requirement.

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Authors and Affiliations

  1. Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, , Israel

    Paz Carmi, Shlomi Dolev & Matthew J. Katz

  2. Department of Computer Science, DCL 2111, University of Illinois, 1304 West Springfield Ave., Urbana, IL 61801, , USA

    Sariel Har-Peled

  3. Department of Communication Systems Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

    Michael Segal

Authors
  1. Paz Carmi
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  2. Shlomi Dolev
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  3. Sariel Har-Peled
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  4. Matthew J. Katz
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  5. Michael Segal
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Corresponding authors

Correspondence to Paz Carmi, Shlomi Dolev, Sariel Har-Peled, Matthew J. Katz or Michael Segal.

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Carmi, P., Dolev, S., Har-Peled, S. et al. Geographic Quorum System Approximations. Algorithmica 41, 233–244 (2005). https://doi.org/10.1007/s00453-004-1130-1

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  • DOI: https://doi.org/10.1007/s00453-004-1130-1

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