A strongly polynomial minimum cost circulation algorithm
Combinatorica
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A faster strongly polynomial minimum cost flow algorithm
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Improved time bounds for the maximum flow problem
SIAM Journal on Computing
Finding minimum-cost circulations by canceling negative cycles
Journal of the ACM (JACM)
Finding minimum-cost circulations by successive approximation
Mathematics of Operations Research
Tight bounds on the number of minimum-mean cycle cancellations and related results
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Dual cancelling algorithms and integrality results for network flow problems
Dual cancelling algorithms and integrality results for network flow problems
Approximate binary search algorithms for mean cuts and cycles
Operations Research Letters
Algorithms for the minimum cost circulation problem based on maximizing the mean improvement
Operations Research Letters
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The problem of minimizing capacity violation is a variation of the transshipment problem. It is equivalent to the problem of computing maximum mean surplus cuts which arises in the dual approach to the minimum cost network circulation problem. McCormick and Ervolina [15] proposed an algorithm which computes a sequence of cuts with increasing mean surpluses, and stops when an optimal one is found. The mean surplus of this cut is equal to the minimum possible maximum capacity violation. McCormick and Ervolina proved that the number of iterations in this algorithm is O(m). One iteration, i.e., finding the subsequent cut, amounts to computing maximum flow in an appropriate network. We prove that the number of iterations in this algorithm is &thgr;(n). This gives the best known upper bound O(n2m) for the problem. We also show a tight analysis of this algorithm for the case with integral capacities and demands, and present some improvements.