Minimum-cost load-balancing partitions

Boris Aronov, Paz Carmi, Matthew J. Katz

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

    Abstract

    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 p 1,... ,p m be m points representing m facilities. We consider the following problem: Subdivide D into m equal-area regions R 1.,..., R m, so that region R i is served by facility p i, 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 = 2 k 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
    Pages301-308
    Number of pages8
    Volume2006
    StatePublished - 2006
    Event22nd Annual Symposium on Computational Geometry 2006, SCG'06 - Sedona, AZ, United States
    Duration: Jun 5 2006Jun 7 2006

    Other

    Other22nd Annual Symposium on Computational Geometry 2006, SCG'06
    CountryUnited States
    CitySedona, AZ
    Period6/5/066/7/06

    Fingerprint

    Load Balancing
    Resource allocation
    Partition
    Costs
    Approximation algorithms
    Optimal Partition
    Subdivide
    Oils and fats
    Average Distance
    Convex polygon
    Voronoi Diagram
    Balancing
    Fats
    Polygon
    Approximation Algorithms
    Maximise
    Requirements

    Keywords

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

    ASJC Scopus subject areas

    • Software
    • Geometry and Topology
    • Safety, Risk, Reliability and Quality
    • Chemical Health and Safety

    Cite this

    Aronov, B., Carmi, P., & Katz, M. J. (2006). Minimum-cost load-balancing partitions. In Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06 (Vol. 2006, pp. 301-308)

    Minimum-cost load-balancing partitions. / Aronov, Boris; Carmi, Paz; Katz, Matthew J.

    Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06. Vol. 2006 2006. p. 301-308.

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

    Aronov, B, Carmi, P & Katz, MJ 2006, Minimum-cost load-balancing partitions. in Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06. vol. 2006, pp. 301-308, 22nd Annual Symposium on Computational Geometry 2006, SCG'06, Sedona, AZ, United States, 6/5/06.
    Aronov B, Carmi P, Katz MJ. Minimum-cost load-balancing partitions. In Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06. Vol. 2006. 2006. p. 301-308
    Aronov, Boris ; Carmi, Paz ; Katz, Matthew J. / Minimum-cost load-balancing partitions. Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06. Vol. 2006 2006. pp. 301-308
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