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Covering a simplex by spheres: complexity and algorithms

Author

Listed:
  • Tongli Zhang

    (Beihang University)

  • Yong Xia

    (Beihang University)

Abstract

Simplex covering optimization problem (SCO) is modeled from the application of covering a simplex by m given balls. It contains the maximin dispersion problem as a special case. In this paper, we prove that (SCO) is NP-hard. We present an enumeration method (EM) to globally solve (SCO) and show that the complexity is strongly polynomial when m is fixed. Numerical experiments demonstrate that EM outperforms CPLEX when m is small. For larger m, we propose an efficient incomplete enumeration method based on linear programming relaxation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:1:d:10.1007_s10898-022-01137-z
    DOI: 10.1007/s10898-022-01137-z
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    References listed on IDEAS

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    1. Erkut, Erhan & Neuman, Susan, 1989. "Analytical models for locating undesirable facilities," European Journal of Operational Research, Elsevier, vol. 40(3), pages 275-291, June.
    2. B. Dasarathy & Lee J. White, 1980. "A Maxmin Location Problem," Operations Research, INFORMS, vol. 28(6), pages 1385-1401, December.
    3. 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.
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