A near-linear time algorithm for constructing a cactus representation of minimum cuts
Author(s)Karger, David R.; Panigrahi, Debmalya
MetadataShow full item record
We present an Õ(m) (near-linear) time Monte Carlo algorithm for constructing the cactus data structure, a useful representation of all the global minimum edge cuts of an undirected graph. Our algorithm represents a fundamental improvement over the best previous (quadratic time) algorithms: because there can be quadratically many min-cuts, our algorithm must avoid looking at all min-cuts during the construction, but nonetheless builds a data structure representing them all. Our result closes the gap between the (near-linear) time required to find a single min-cut and that for (implicitly) finding all the min-cuts.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Society for Industrial and Applied Mathematics
Karger, D. R. and Panigrahi, D. 2009. A near-linear time algorithm for constructing a cactus representation of minimum cuts. In Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms (New York, New York, January 04 - 06, 2009). Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, 246-255. (C)2009 Society for Industrial and Applied Mathematics.
Final published version