On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks.
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| Title: | On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks. |
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| Authors: | Nguyen, Kien Trung1 trungkien@ctu.edu.vn, Nguyen-Thu, Huong1 nthuong@ctu.edu.vn, Hung, Nguyen Thanh1 nthung@ctu.edu.vn |
| Source: | Mathematical Methods of Operations Research. Oct2018, Vol. 88 Issue 2, p147-159. 13p. 2 Diagrams. |
| Subjects: | Location theory (Geography), Planes (Hand tools), Trees, Multipliers (Mathematical analysis), Economic geography |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| 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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 14322994 |
| DOI: | 10.1007/s00186-018-0632-6 |
