| Issue |
RAIRO-Oper. Res.
Volume 42, Number 3, July-September 2008
|
|
|---|---|---|
| Page(s) | 401 - 414 | |
| DOI | https://doi.org/10.1051/ro:2008017 | |
| Published online | 20 August 2008 | |
The inverse maximum flow problem considering l∞ norm
University “Transilvania” of Brasov, Faculty of Mathematics and Informatics, Theoretical Computer Science Departement, str. Iuliu Maniu 50, Brasov, Romania; a.deaconu@unitbv.ro
Received:
7
September
2006
Accepted:
28
March
2008
The problem is to modify the capacities of the arcs from a network so that a given feasible flow becomes a maximum flow and the maximum change of the capacities on arcs is minimum. A very fast O(m⋅log(n)) time complexity algorithm for solving this problem is presented, where m is the number of arcs and n is the number of nodes of the network. The case when both, lower and upper bounds of the flow can be modified so that the given feasible flow becomes a maximum flow is also discussed. The algorithm proposed can be adapted to solve this problem, too. The inverse minimum flow problem considering l∞ norm is also studied.
Mathematics Subject Classification: 90C27 / 90C35 / 68R10
Key words: Inverse combinatorial optimization / maximum flow / strongly polynomial time complexity.
© EDP Sciences, ROADEF, SMAI, 2008
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