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Combinatorial Algorithms for Reverse Selective Undesirable Center Location Problems on Cycle Graphs

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Abstract

This paper deals with a general variant of the reverse undesirable (obnoxious) center location problem on cycle graphs. Given a ‘selective’ subset of the vertices of the underlying cycle graph as location of the existing customers, the task is to modify the edge lengths within a given budget such that the minimum of distances between a predetermined undesirable facility location and the customer points is maximized under the perturbed edge lengths. We develop a combinatorial \(\mathcal {O}(n\log n)\) algorithm for the problem with continuous modifications. For the uniform-cost model, we solve this problem in linear time by an improved algorithm. Furthermore, exact solution methods are proposed for the problem with integer modifications.

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Acknowledgements

The authors are grateful to anonymous referees for their helpful comments.

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Correspondence to Behrooz Alizadeh.

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This work was partially supported by the Sahand University of Technology under the Ph.D. program contract (No. 30/15971).

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Etemad, R., Alizadeh, B. Combinatorial Algorithms for Reverse Selective Undesirable Center Location Problems on Cycle Graphs. J. Oper. Res. Soc. China 5, 347–361 (2017). https://doi.org/10.1007/s40305-016-0144-0

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  • DOI: https://doi.org/10.1007/s40305-016-0144-0

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