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On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks

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Abstract

An ordered median function is used in location theory to generalize a class of problems, including median and center problems. In this paper we consider the complexity of inverse ordered 1-median problems on the plane and on trees, where the multipliers are sorted nondecreasingly. Based on the convexity of the objective function, we prove that the problems with variable weights or variable coordinates on the line are NP-hard. Then we can directly get the NP-hardness result for the corresponding problem on the plane. We finally develop a cubic time algorithm that solves the inverse convex ordered 1-median problem on trees with relaxation on modification bounds.

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Acknowledgements

The authors would like to thank the anonymous referees and editors for their comments, which helped to improve the organization of this paper significantly.

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Authors and Affiliations

  1. Mathematics Department, Teacher College, Can Tho University, Can Tho, Vietnam

    Kien Trung Nguyen, Huong Nguyen-Thu & Nguyen Thanh Hung

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  1. Kien Trung Nguyen
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  2. Huong Nguyen-Thu
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  3. Nguyen Thanh Hung
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Correspondence to Kien Trung Nguyen.

Additional information

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2016.08.

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Nguyen, K.T., Nguyen-Thu, H. & Hung, N.T. On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks. Math Meth Oper Res 88, 147–159 (2018). https://doi.org/10.1007/s00186-018-0632-6

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  • DOI: https://doi.org/10.1007/s00186-018-0632-6

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