Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Approximating s-t minimum cuts in Õ(n2) time
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Using random sampling to find maximum flows in uncapacitated undirected graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Finding maximum flows in undirected graphs seems easier than bipartite matching
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Flows in Undirected Unit Capacity Networks
SIAM Journal on Discrete Mathematics
Random sampling in residual graphs
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
| Hi-index | 0.89 |
Let D=(V,E) be a simple digraph with n vertices and m edges, and s and t be vertices designated as a source and a sink. The currently fastest algorithm that computes a minimum (s,t)-cut in D runs in O(min{@n,n^2^/^3,m^1^/^2}m) time, where @n is the size of a minimum (s,t)-cut. In this paper, we define the non-eulerianness @m as the sum of |#incoming edges at u-#outgoing edges at u| over all u@?V-{s,t}, and prove that a minimum (s,t)-cut in D can be obtained in O(min{m+@n(@n+@m)^1^/^2n,(@n+@m)^1^/^6nm^2^/^3}) time. This outperforms the previous algorithm when D is a dense digraph with small @m.