2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1997)
Miami Beach, FL
Oct. 19, 1997 to Oct. 22, 1997
S. Rao , NEC Res. Inst., Princeton, NJ, USA
A.V. Goldberg , NEC Res. Inst., Princeton, NJ, USA
We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual are capacities. Our approach leads to an O(min(n/sup 2/3/, m/sup 1/2/)m log(n/sup 2//m) log U) time bound for a network with n vertices, m arcs, and integral arc capacities in the range [1,...,U]. This is a fundamental improvement over the previous time bounds. We also improve bounds for the Gomory-Hu tree problem, the parametric flow problem, and the approximate s-t cut problems.
combinatorial mathematics; flow decomposition barrier; maximum flow problem; arc lengths; time bound; Gomory-Hu tree problem; parametric flow problem; time bounds
S. Rao, A.V. Goldberg, "Beyond the flow decomposition barrier", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 2, 1997, doi:10.1109/SFCS.1997.646087