The inverse 1-center problem on cycles with variable edge lengths
Kien Trung Nguyen ()
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Kien Trung Nguyen: Can Tho University
Central European Journal of Operations Research, 2019, vol. 27, issue 1, 263-274
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 $$O(n^2 \log n)$$ O ( n 2 log n ) time, where n is the number of vertices in the cycle.
Keywords: 1-Center problem; Inverse optimization; Cycle; Convex; Parameterization; 90B10; 90B80; 90C27 (search for similar items in EconPapers)
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