On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks

Kien Trung Nguyen (), Huong Nguyen-Thu () and Nguyen Thanh Hung ()
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Kien Trung Nguyen: Can Tho University
Huong Nguyen-Thu: Can Tho University
Nguyen Thanh Hung: Can Tho University

Mathematical Methods of Operations Research, 2018, vol. 88, issue 2, No 1, 147-159

Abstract: Abstract An ordered median function is used in location theory to generalize a class of problems, including median and center problems. In this paper we consider the complexity of inverse ordered 1-median problems on the plane and on trees, where the multipliers are sorted nondecreasingly. Based on the convexity of the objective function, we prove that the problems with variable weights or variable coordinates on the line are NP-hard. Then we can directly get the NP-hardness result for the corresponding problem on the plane. We finally develop a cubic time algorithm that solves the inverse convex ordered 1-median problem on trees with relaxation on modification bounds.

Keywords: Ordered median; Inverse location; Complexity; Convex; Tree (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-018-0632-6

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