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

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  • Kien Trung Nguyen

    (Teacher College, Can Tho University)

  • Nguyen Thanh Hung

    (Teacher College, Can Tho University)

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 $$O(n\log n)$$ O ( n log n ) time, where n is the number of vertices in the underlying block graph.

Suggested Citation

  • Kien Trung Nguyen & Nguyen Thanh Hung, 2020. "The inverse connected p-median problem on block graphs under various cost functions," Annals of Operations Research, Springer, vol. 292(1), pages 97-112, September.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:1:d:10.1007_s10479-020-03651-3
    DOI: 10.1007/s10479-020-03651-3
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    References listed on IDEAS

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