Inverse bottleneck optimization problems on networks

Authors:
Xiucui Guan;Jianzhong Zhang
Affiliations:
Department of Mathematics, Southeast University, Nanjing, P.R. China;Department of System Engineering and Engineering Management, Chinese University of Hong Kong, Hong Kong, P. R. China
Venue:
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Year:
2006

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Abstract

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 l1 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 l1 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|.