Inverse Maximum Flow Problem Under the Combination of the Weighted l\(_2\) Norm and the Weighted Hamming Distance
- 2 Downloads
The idea of the inverse optimization problem is to adjust the values of the parameters so that the observed feasible solutions are indeed optimal. The modification cost is measured by different norms, such as \(l_1, l_2, l_\infty \) norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse maximum flow problem under the combination of the weighted \(l_2\) norm and the weighted Hamming distance, i.e., the modification cost is fixed in a given interval and depends on the modification out of the given interval. We present a combinatorial algorithm which can be finished in O(nm) to solve it due to the minimum cut of the residual network.
KeywordsMaximum flow Minimum cut Inverse problem Residual network Strongly polynomial algorithm
Mathematics Subject Classification05C21 68Q25 90B10 90C27
The authors wish to thank the anonymous referees whose valuable comments allowed us to improve the paper.
- 1.Ahuja, R.K., Magnant, T.L., Orlin, J.B.: Network Flows: Theory. Algorithms and Applications. Prentice-Hall, Englewood Cliffs (1993)Google Scholar
- 21.Orlin, J.B.: Max flows in \(O(nm)\) time, or better. In: Proceeding of annual ACM symposium on theory of computing, pp. 765–774 (2013)Google Scholar