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The two-center problem of uncertain points on a real line

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  • Haitao Xu

    (Cleveland State University)

  • Jingru Zhang

    (Cleveland State University)

Abstract

Facility location problems on uncertain demand data have attracted significant attention recently. In this paper, we consider the two-center problem on uncertain points on a real line. The input is a set $$\mathcal {P}$$ P of n uncertain points on the line. Each uncertain point is represented by a probability density function that is a piecewise uniform distribution (i.e., a histogram) of complexity m. The goal is to find two points (centers) on the line so that the maximum expected distance of all uncertain points to their expected closest centers is minimized. A previous algorithm for the uncertain k-center problem can solve this problem in $$O(mn\log mn + n\log ^2n)$$ O ( m n log m n + n log 2 n ) time. In this paper, we propose a more efficient algorithm solving it in $$O(mn\log m+n\log n)$$ O ( m n log m + n log n ) time. Besides, we give an algorithm of the same time complexity for the discrete case where each uncertain point follows a discrete distribution.

Suggested Citation

  • Haitao Xu & Jingru Zhang, 2023. "The two-center problem of uncertain points on a real line," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-22, March.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:2:d:10.1007_s10878-023-00996-w
    DOI: 10.1007/s10878-023-00996-w
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    References listed on IDEAS

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    1. Wang, Haitao, 2014. "Minmax regret 1-facility location on uncertain path networks," European Journal of Operational Research, Elsevier, vol. 239(3), pages 636-643.
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