Scaling algorithms for network problems
Journal of Computer and System Sciences
A strongly polynomial minimum cost circulation algorithm
Combinatorica
Discrete Applied Mathematics
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Finding minimum-cost circulations by successive approximation
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Finding minimum-cost flows by double scaling
Mathematical Programming: Series A and B
On the computational behavior of a polynomial-time network flow algorithm
Mathematical Programming: Series A and B
A faster strongly polynomial minimum cost flow algorithm
Operations Research
Polynomial dual network simplex algorithms
Mathematical Programming: Series A and B
A faster combinatorial algorithm for the generalized circulation problem
Mathematics of Operations Research
Polynomial-time highest-gain augmenting path algorithms for the generalized circulation problem
Mathematics of Operations Research
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
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In this paper, we present a new polynomial time algorithm for solving the minimum cost network flow problem. This algorithm is based on Edmonds-Karp's capacity scaling and Orlin's excess scaling algorithms. Unlike these algorithms, our algorithm works directly with the given data and original network, and dynamically adjusts the scaling factor between scaling phases, so that it performs at least one flow augmentation in each phase. Our algorithm has a complexity of O(m(m+nlogn)log(B/(m+n))), where n is the number of nodes, m is the number of arcs, and B is the sum of the finite arc capacities and supplies in the network.