Inverse Bottleneck Optimization Problems on Networks
The bottleneck optimization problem is to find a feasible solution that minimizes the bottleneck cost. In this paper, we consider the inverse bottleneck optimization problems with bound constraints on modification under weighted l 1 norm, weighted sum-Hamming distance and weighted bottleneck-Hamming distance. That is, given a feasible solution F *, we aim to modify the cost function under some measure such that F * becomes an optimal solution to the bottleneck optimization problem. We show that the inverse problem under weighted l 1 norm and weighted sum-Hamming distance can be reduced to O(m) minimum cut problems, while the inverse problem under weighted bottleneck-Hamming distance can be reduced to O(logm) cut feasibility problems, where m = |E|.
KeywordsInverse Problem Feasible Solution Span Tree Problem Capacity Vector Isotonic Regression
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