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The inverse connected p-median problem on block graphs under various cost functions
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Journal Article
The inverse connected p-median problem on block graphs under various cost functions
2020
Overview
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(nlogn) time, where n is the number of vertices in the underlying block graph.
Publisher
Springer Nature B.V
