Please use this identifier to cite or link to this item: https://dspace.ctu.edu.vn/jspui/handle/123456789/5110
Title: The inverse 1-center problem on cycles with variable edge lengths
Authors: Nguyễn, Trung Kiên
Keywords: 1-Center problem
Inverse optimization
Cycle
Convex
Parameteri-zation
Issue Date: 2017
Series/Report no.: Central European Journal of Operations Research;1 .- p.1-12
Abstract: We consider the problem of modifying edge lengths of a cycle at minimum total costs so as to make a prespecified vertex an (absolute) 1-center of the cycle with respect to the new edge legths.We call this problem the inverse 1-center problem on a cycle. To solve this problem, we first construct the so-called optimality criterion for a vertex to be a 1-center. Based on the optimality criterion, it is shown that the problem can be separated into linearly many subproblems. For a predetermined subproblem, we apply a parameterization approach to formulate it as a minimization problem of a piecewise linear convex function with a connected feasible region. Hence, it is shown that the problem can be solved in O(n² log n) time, where n is the number of vertices in the cycle.
URI: http://localhost:8080//jspui/handle/123456789/5110
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