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The Euclidean k -Supplier Problem

Author

Listed:
  • Viswanath Nagarajan

    (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109;)

  • Baruch Schieber

    (IBM T.J. Watson Research Center, Yorktown Heights, New York 10598;)

  • Hadas Shachnai

    (Computer Science Department, Technion, Haifa, Israel 3200003)

Abstract

The k -supplier problem is a fundamental location problem that involves opening k facilities to minimize the maximum distance of any client to an open facility. We consider the k -supplier problem in Euclidean metrics (of arbitrary dimension) and present an algorithm with approximation ratio 1 + 3 < 2.74 . This improves upon the previously known 3-approximation algorithm, which also holds for general metrics. Our result is almost best possible as the Euclidean k -supplier problem is NP-hard to approximate better than a factor of 7 > 2.64 . We also present a nearly linear time algorithm for the Euclidean k -supplier in constant dimensions that achieves an approximation ratio better than three.

Suggested Citation

  • Viswanath Nagarajan & Baruch Schieber & Hadas Shachnai, 2020. "The Euclidean k -Supplier Problem," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 1-14, February.
    • Handle: RePEc:inm:ormoor:v:45:y:2020:i:1:p:1-14
    DOI: 10.1287/moor.20180953
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    References listed on IDEAS

    as
    1. Mark S. Daskin & Lawrence V. Snyder & Rosemary T. Berger, 2005. "Facility Location in Supply Chain Design," Springer Books, in: André Langevin & Diane Riopel (ed.), Logistics Systems: Design and Optimization, chapter 0, pages 39-65, Springer.
    2. Ravishankar Krishnaswamy & Amit Kumar & Viswanath Nagarajan & Yogish Sabharwal & Barna Saha, 2015. "Facility Location with Matroid or Knapsack Constraints," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 446-459, February.
    3. Dorit S. Hochbaum & David B. Shmoys, 1985. "A Best Possible Heuristic for the k -Center Problem," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 180-184, May.
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