Abstract
This paper addresses the problem of optimally modifying the edge lengths such that a prespecified vertex becomes the furthest vertex from a given fixed vertex in the perturbed network. We call this problem the inverse eccentric vertex problem. We show that the problem is \(NP\)-complete even on cactus graphs. However, if the underlying graph is a cycle or a tree, we develop efficient algorithms with linear time complexity.
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Acknowledgments
The authors would like to thank anonymous referees for helpful feedback that helped to improve the paper. This work was financial supported by DAAD (German Academic Exchange Service).
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Nguyen, K.T., Chassein, A. Inverse eccentric vertex problem on networks. Cent Eur J Oper Res 23, 687–698 (2015). https://doi.org/10.1007/s10100-014-0367-2
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DOI: https://doi.org/10.1007/s10100-014-0367-2