A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
A primal simplex algorithm that solves the maximum flow problem in at most nm pivots and o(n2m) time
Mathematical Programming: Series A and B
On strongly polynomial dual simplex algorithms for the maximum flow problem
Mathematical Programming: Series A and B
Optimal Net Surface Problems with Applications
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
A survey of graph theoretical approaches to image segmentation
Pattern Recognition
Push-relabel based algorithms for the maximum transversal problem
Computers and Operations Research
GPU accelerated maximum cardinality matching algorithms for bipartite graphs
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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We introduce an algorithm that solves the maximum flow problem without generating flows explicitly. The algorithm solves directly a problem we call the maximum s-excess problem. That problem is equivalent to the minimum cut problem, and is a direct extension of the maximum closure problem. The concepts used also lead to a new parametric analysis algorithm generating all breakpoints in the amount of time of a single run. The insights derived from the analysis of the new algorithm lead to a new simplex algorithm for the maximum flow problem - a pseudoflow-based simplex. We show that this simplex algorithm can perform a parametric analysis in the same amount of time as a single run. This is the first known simplex algorithm for maximum flow that generates all possible breakpoints of parameter values in the same complexity as required to solve a single maximum flow instance and the fastest one. The complexities of our pseudoflow algorithm, the new simplex algorithm, and the parametric analysis for both algorithms are O(mnlog n) on a graph with n nodes and m arcs.