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New Approximation Algorithms for Weighted Maximin Dispersion Problem with Box or Ball Constraints

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  • Siwen Wang

    (Shanghai University)

  • Zi Xu

    (Shanghai University)

Abstract

In this paper, we propose new approximation algorithms for a NP-hard problem, i.e., weighted maximin dispersion problem. By using a uniformly distributed random sample method, we first propose a new random approximation algorithm for box constrained or ball constrained weighted maximin dispersion problems and analyze its approximation bound respectively. Moreover, we propose two improved approximation algorithms by combining our technique with an existing binary sample technique for both cases. To the best of our knowledge, they are the best approximation bounds for both box constrained and ball constrained weighted maximin dispersion problems respectively.

Suggested Citation

  • Siwen Wang & Zi Xu, 2021. "New Approximation Algorithms for Weighted Maximin Dispersion Problem with Box or Ball Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 524-539, August.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:2:d:10.1007_s10957-021-01893-0
    DOI: 10.1007/s10957-021-01893-0
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    References listed on IDEAS

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    1. S. S. Ravi & D. J. Rosenkrantz & G. K. Tayi, 1994. "Heuristic and Special Case Algorithms for Dispersion Problems," Operations Research, INFORMS, vol. 42(2), pages 299-310, April.
    2. Weiwei Pan & Jingjing Shen & Zi Xu, 2021. "An efficient algorithm for nonconvex-linear minimax optimization problem and its application in solving weighted maximin dispersion problem," Computational Optimization and Applications, Springer, vol. 78(1), pages 287-306, January.
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    Cited by:

    1. Tongli Zhang & Yong Xia, 2022. "Covering a simplex by spheres: complexity and algorithms," Journal of Global Optimization, Springer, vol. 84(1), pages 119-135, September.

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