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

Pham Van Huy () and Nguyen Chi Tam ()
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Pham Van Huy: Ton Duc Thang University
Nguyen Chi Tam: Can Tho University

OPSEARCH, 2019, vol. 56, issue 3, No 8, 780-789

Abstract: 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.

Keywords: Location problem; Ordered 1-median; Cactus; Convex (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s12597-019-00402-2

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