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Algorithms for connected p-centdian problem on block graphs

Author

Listed:
  • Liying Kang

    (Shanghai University)

  • Jianjie Zhou

    (Shanghai University)

  • Erfang Shan

    (Shanghai University)

Abstract

We consider the facility location problem of locating a set $$X_p$$ X p of p facilities (resources) on a network (or a graph) such that the subnetwork (or subgraph) induced by the selected set $$X_p$$ X p is connected. Two problems on a block graph G are proposed: one problem is to minimizes the sum of its weighted distances from all vertices of G to $$X_p$$ X p , another problem is to minimize the maximum distance from each vertex that is not in $$X_p$$ X p to $$X_p$$ X p and, at the same time, to minimize the sum of its distances from all vertices of G to $$X_p$$ X p . We prove that the first problem is linearly solvable on block graphs with unit edge length. For the second problem, it is shown that the set of Pareto-optimal solutions of the two criteria has cardinality not greater than n, and can be obtained in $$O(n^2)$$ O ( n 2 ) time, where n is the number of vertices of the block graph G.

Suggested Citation

  • Liying Kang & Jianjie Zhou & Erfang Shan, 2018. "Algorithms for connected p-centdian problem on block graphs," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 252-263, July.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:1:d:10.1007_s10878-016-0058-0
    DOI: 10.1007/s10878-016-0058-0
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Trung Kien Nguyen & Nguyen Thanh Hung & Huong Nguyen-Thu, 2020. "A linear time algorithm for the p-maxian problem on trees with distance constraint," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1030-1043, November.

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