A strongly polynomial minimum cost circulation algorithm
Combinatorica
Mathematical Programming: Series A and B
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A strongly polynomial algorithm for minimum cost submodular flow problems
Mathematics of Operations Research
Finding minimum-cost circulations by canceling negative cycles
Journal of the ACM (JACM)
Negative circuits for flows and submodular flows
Discrete Applied Mathematics
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Two strongly polynomial cut cancelling algorithms for minimum cost network flow
Discrete Applied Mathematics
Discrete Applied Mathematics
A capacity scaling algorithm for convex cost submodular flows
Mathematical Programming: Series A and B
Polynomial Methods for Separable Convex Optimization in Unimodular Linear Spaces with Applications
SIAM Journal on Computing
Mathematical Programming: Series A and B
A faster algorithm for minimum cost submodular flows
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Relaxed Most Negative Cycle and Most Positive Cut Canceling Algorithms for Minimum Cost Flow
Mathematics of Operations Research
Newton's method for fractional combinatorial optimization
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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This paper presents a new strongly polynomial cut canceling algorithm for minimum cost submodular flow. The algorithm is a generalization of our similar cut canceling algorithm for ordinary mincost flow. The advantage of cut canceling over cycle canceling is that cut canceling seems to generalize to other problems more readily than cycle canceling. The algorithm scales a relaxed optimality parameter, and creates a second, inner relaxation that is a kind of submodular max flow problem. The outer relaxation uses a novel technique for relaxing the submodular constraints that allows our previous proof techniques to work. The algorithm uses the min cuts from the max flow subproblem as the relaxed most positive cuts it chooses to cancel. We show that this algorithm needs to cancel only O(n3) cuts per scaling phase, where n is the number of nodes. Furthermore, we also show how to slightly modify this algorithm to get a strongly polynomial running time.