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The inverse maximum flow problem considering l ∞ norm

Published online by Cambridge University Press:  20 August 2008

Adrian Deaconu
Adrian Deaconu*
Affiliation:
University “Transilvania” of Brasov, Faculty of Mathematics and Informatics, Theoretical Computer Science Departement, str. Iuliu Maniu 50, Brasov, Romania; a.deaconu@unitbv.ro
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Abstract

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.

Keywords

Inverse combinatorial optimizationmaximum flowstrongly polynomial time complexity.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 3 , July 2008 , pp. 401 - 414
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

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