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The Uniform Cost Reverse 1-Centdian Location Problem on Tree Networks with Edge Length Reduction

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Abstract

In location theory, the 1-centdian function is a convex combination of the 1-median and the 1-center functions. We consider the uniform cost reverse 1-centdian problem on networks, where edge lengths are reduced within a given budget such that the 1-centdian function at a prespecified point on the network is minimized. We first prove that the problem on general networks is NP-hard by reducing the set cover problem to it. Then, we focus on the special case of the problem on tree networks. Based on the strategy that we reduce either one edge or several edges simultaneously in each step to obtain an optimal solution, we develop a combinatorial algorithm that solves the corresponding problem on trees in quadratic time.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2019.325. The authors would like to acknowledge anonymous referees for their valuable suggestions which helped to improve the paper.

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Authors and Affiliations

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

    Kien Trung Nguyen

  2. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, USM, Malaysia

    Wen Chean Teh

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  1. Kien Trung Nguyen
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  2. Wen Chean Teh
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Correspondence to Kien Trung Nguyen.

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Nguyen, K.T., Teh, W.C. The Uniform Cost Reverse 1-Centdian Location Problem on Tree Networks with Edge Length Reduction. Vietnam J. Math. 51, 345–361 (2023). https://doi.org/10.1007/s10013-021-00529-0

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  • DOI: https://doi.org/10.1007/s10013-021-00529-0

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