Minimum-cost load-balancing partitions

Boris Aronov, Paz Carmi, Matthew J. Katz

    Research output: Chapter in Book/Report/Conference proceedingConference contribution


    We consider the problem of balancing the load among several service-providing facilities, while keeping the total cost low. Let D be the underlying demand region, and let p1,... ,pm be m points representing m facilities. We consider the following problem: Subdivide D into m equal-area regions R1.,..., Rm, so that region R i is served by facility pi, and the average distance between a point q in D and the facility that serves q is minimal. We present constant-factor approximation algorithms for this problem, with the additional requirement that the resulting regions must be convex. As an intermediate result we show how to partition a convex polygon into m = 2k equal-area convex subregions so that the fatness of the resulting regions is within a constant factor of the fatness of the original polygon. We also prove that our partition is, up to a constant factor, the best one can get if one's goal is to maximize the fatness of the least fat subregion. We also discuss the structure of the optimal partition for the aforementioned load balancing problem: indeed, we argue that it is always induced by an additive-weighted Voronoi diagram for an appropriate choice of weights.

    Original languageEnglish (US)
    Title of host publicationProceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06
    PublisherAssociation for Computing Machinery (ACM)
    Number of pages8
    ISBN (Print)1595933409, 9781595933409
    StatePublished - 2006
    Event22nd Annual Symposium on Computational Geometry 2006, SCG'06 - Sedona, AZ, United States
    Duration: Jun 5 2006Jun 7 2006

    Publication series

    NameProceedings of the Annual Symposium on Computational Geometry


    Other22nd Annual Symposium on Computational Geometry 2006, SCG'06
    Country/TerritoryUnited States
    CitySedona, AZ


    • Additive-weighted Voronoi diagrams
    • Approximation algorithms
    • Fat partitions
    • Fatness
    • Geometric optimization
    • Load balancing

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Computational Mathematics


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