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A combinatorial algorithm for the ordered 1-median problem on cactus graphs

Author

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  • Van Huy Pham

    (Ton Duc Thang University)

  • Nguyen Chi Tam

    (Can Tho University)

Abstract

Cactus graph is a graph in which any two simple cycles has at most one vertex in common. In this paper we address the ordered 1-median location problem on cactus graphs, a generalization of some popular location models such as 1-median, 1-center, and 1-centdian problems. For the case with non-decreasing multipliers, we show that there exists a cycle or an edge that contains an ordered 1-median. Based on this property, we develop a combinatorial algorithm that finds an ordered 1-median on a cactus in $$O(n^2\log n)$$ O ( n 2 log n ) time, where n is the number of vertices in the underlying cactus.

Suggested Citation

  • Van Huy Pham & Nguyen Chi Tam, 2019. "A combinatorial algorithm for the ordered 1-median problem on cactus graphs," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 780-789, September.
    • Handle: RePEc:spr:opsear:v:56:y:2019:i:3:d:10.1007_s12597-019-00402-2
    DOI: 10.1007/s12597-019-00402-2
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