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Geometric partitioning and robust ad-hoc network design

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  • John Carlsson
  • Mehdi Behroozi
  • Xiang Li

Abstract

We present fast approximation algorithms for the problem of dividing a given convex geographic region into smaller sub-regions so as to distribute the workloads of a set of vehicles. Our objective is to partition the region in such a fashion as to ensure that vehicles are capable of communicating with one another under limited communication radii. We consider variations of this problem in which sub-regions are constrained to have equal area or be convex, and as a side consequence, our approach yields a factor 1.99 approximation algorithm for the continuous k-centers problem on a convex polygon. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • John Carlsson & Mehdi Behroozi & Xiang Li, 2016. "Geometric partitioning and robust ad-hoc network design," Annals of Operations Research, Springer, vol. 238(1), pages 41-68, March.
    • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:p:41-68:10.1007/s10479-015-2093-0
    DOI: 10.1007/s10479-015-2093-0
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    References listed on IDEAS

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    1. J. Brimberg & S. Salhi, 2005. "A Continuous Location-Allocation Problem with Zone-Dependent Fixed Cost," Annals of Operations Research, Springer, vol. 136(1), pages 99-115, April.
    2. Haugland, Dag & Ho, Sin C. & Laporte, Gilbert, 2007. "Designing delivery districts for the vehicle routing problem with stochastic demands," European Journal of Operational Research, Elsevier, vol. 180(3), pages 997-1010, August.
    3. Oded Berman & Zvi Drezner & Arie Tamir & George Wesolowsky, 2009. "Optimal location with equitable loads," Annals of Operations Research, Springer, vol. 167(1), pages 307-325, March.
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    Cited by:

    1. Mehdi Behroozi, 2024. "Largest Volume Inscribed Rectangles in Convex Sets Defined by Finite Number of Inequalities," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 787-819, May.

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