Abstract
This paper concerns with some variants of the inverse obnoxious median location problem on tree networks, where the aim is either to augment or to reduce the edge lengths at the minimum total cost such that a prespecified subset of vertices becomes an obnoxious multi-facility median location with respect to the perturbed edge lengths. For both augmentation and reduction models, under the rectilinear norm and the sum-type Hamming distance, we develop novel combinatorial algorithms with polynomial time complexities. Particularly, if the underlying tree is an extended star graph, then the problems can be solved in linear time.
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The authors would like to thank the editor-in-chief and anonymous reviewers for their helpful and constructive comments, which helped us to improve the paper.
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Communicated by Alexander Martin.
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Alizadeh, B., Afrashteh, E. & Baroughi, F. Combinatorial Algorithms for Some Variants of Inverse Obnoxious Median Location Problem on Tree Networks. J Optim Theory Appl 178, 914–934 (2018). https://doi.org/10.1007/s10957-018-1334-1
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DOI: https://doi.org/10.1007/s10957-018-1334-1