Solving the Convex Cost Integer Dual Network Flow Problem
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The base-matroid and inverse combinatorial optimization problems
Discrete Applied Mathematics
Solving the Convex Cost Integer Dual Network Flow Problem
Management Science
WSEAS Transactions on Computers
Transfomation of non-feasible inverse maximum flow problem into a feasible one by flow modification
ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume I
A study on the feasibility of the inverse supply and demand problem
Proceedings of the 15th WSEAS international conference on Computers
Inverse problems of some NP-complete problems
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Inverse conic programming with applications
Operations Research Letters
Note: Inverse multi-objective combinatorial optimization
Discrete Applied Mathematics
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Given a solution x* and an a priori estimated cost vector c, the inverse optimization problem is to identify another cost vector d so that x* is optimal with respect to the cost vector d and its deviation from c is minimum. In this paper, we consider the inverse spanning tree problem on an undirected graph G = (N, A) with n nodes and m arcs, and where the deviation between c and d is defined by the rectilinear distance between the two vectors, that is, L1 norm. We show that the inverse spanning tree problem can be formulated as the dual of an assignment problem on a bipartite network G0 = (N0, A0) with [math not displayed] and [math not displayed]. The bipartite ne twork satisfies the property that |N1| = (n - 1), |N2| = (m - n + 1), and |A0| = O(nm). In general, |N1| N2|. Using this special structure of the assignment problem, we develop a specific implementation of the successive shortest path algorithm that runs in O(n3) time. We also consider the weighted version of the inverse spanning tree problem in which the objective function is to minimize the sum of the weighted deviations of arcs. The weighted inverse spanning tree can be formulated as the dual of the transportation problem. Using a cost scaling algorithm, this transportation problem can be solved in O(n2m log(nC)) time, where C denotes the largest arc cost in the data. Finally, we consider a minimax version of the inverse spanning tree problem and show that it can be solved in O(n2) time.