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April, 2020 Inverse Anti-$k$-centrum Problem on Networks with Variable Edge Lengths
Van Huy Pham, Kien Trung Nguyen
Taiwanese J. Math. 24(2): 501-522 (April, 2020). DOI: 10.11650/tjm/190602


This paper concerns the problem of modifying edge lengths of a network at minimum total costs so as to make a prespecified vertex become an optimal location in the modified environment. Here, we focus on the ordered median objective function with respect to the vector of multipliers $\lambda = (1,\ldots,1,0,\ldots,0)$ with $k$ 1's. This problem is called the inverse anti-$k$-centrum problem. We first show that the inverse anti-$k$-centrum problem is NP-hard even on tree networks. However, for the inverse anti-$k$-centrum problem on cycles, we formulate it as one or two linear programs, depending on odd or even integer $k$. Concerning the special cases with $k = 2,3,M$, we develop combinatorial algorithms that efficiently solve the problem, where $M$ is the number of vertices of the cycle.


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Van Huy Pham. Kien Trung Nguyen. "Inverse Anti-$k$-centrum Problem on Networks with Variable Edge Lengths." Taiwanese J. Math. 24 (2) 501 - 522, April, 2020.


Received: 4 December 2018; Revised: 30 May 2019; Accepted: 13 June 2019; Published: April, 2020
First available in Project Euclid: 21 June 2019

zbMATH: 07192945
MathSciNet: MR4078208
Digital Object Identifier: 10.11650/tjm/190602

Primary: 90B10, 90B80, 90C27

Rights: Copyright © 2020 The Mathematical Society of the Republic of China


Vol.24 • No. 2 • April, 2020
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