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The inverse connected p-median problem on block graphs under various cost functions

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Abstract

We address the problem of modifying vertex weights of a block graph at minimum total cost so that a predetermined set of p connected vertices becomes a connected p-median on the perturbed block graph. This problem is the so-called inverse connected p-median problem on block graphs. We consider the problem on a block graph with uniform edge lengths under various cost functions, say rectilinear norm, Chebyshev norm, and bottleneck Hamming distance. To solve the problem, we first find an optimality criterion for a set that is a connected p-median. Based on this criterion, we can formulate the problem as a convex or quasiconvex univariate optimization problem. Finally, we develop combinatorial algorithms that solve the problems under the three cost functions in \(O(n\log n)\) time, where n is the number of vertices in the underlying block graph.

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Acknowledgements

We would like to acknowledge anonymous referees for their valuable remarks and comments which have helped to improve the paper significantly. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2019.325.

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  1. Department of Mathematics, Teacher College, Can Tho University, 3/2 Street, Xuan Khanh District, Can Tho, Vietnam

    Kien Trung Nguyen & Nguyen Thanh Hung

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  1. Kien Trung Nguyen
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  2. Nguyen Thanh Hung
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Correspondence to Kien Trung Nguyen.

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Nguyen, K.T., Hung, N.T. The inverse connected p-median problem on block graphs under various cost functions. Ann Oper Res 292, 97–112 (2020). https://doi.org/10.1007/s10479-020-03651-3

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