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JCO
2010

Capacity inverse minimum cost flow problem

13 years 10 months ago
Capacity inverse minimum cost flow problem
Given a directed graph G = (N, A) with arc capacities uij and a minimum cost flow problem defined on G, the capacity inverse minimum cost flow problem is to find a new capacity vector ˆu for the arc set A such that a given feasible solution ˆx is optimal with respect to the modified capacities. Among all capacity vectors ˆu satisfying this condition, we would like to find one with minimum ˆu − u value. We consider two distance measures for ˆu − u , rectilinear (L1) and chebyshev (L∞) distances. By reduction from the feedback arc set problem we show that the capacity inverse minimum cost flow problem is NP-hard in the rectilinear case. On the other hand, it is polynomially solvable by a greedy algorithm for the chebyshev norm. In the latter case we also propose a heuristic for the bicriteria problem, where we minimize among all optimal solutions the number of affected arcs.
Çigdem Güler, Horst W. Hamacher
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JCO
Authors Çigdem Güler, Horst W. Hamacher
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