Computing vertex connectivity: New bounds from old techniques
- Digital Equipment Corp., Palo Alto, CA (United States)
- NEC Research Institute, Princeton, NJ (United States)
- Univ. of Colorado, Boulder, CO (United States)
The vertex connectivity {kappa} of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{kappa}{sup 3} + n, {kappa}nm); for an undirected graph the term m can be replaced by {kappa}n. A randomized algorithm finds {kappa} with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O({kappa}{sub 1}nm log(n{sup 2}/m)) where {kappa}{sub 1} < m/n is the unweighted vertex connectivity, or in expected time O(nm log (n{sup 2}/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin [HO] that computes edge connectivity.
- OSTI ID:
- 457676
- Report Number(s):
- CONF-961004--; CNN: Grant CCR-9501712; Grant CCR-9215199
- Country of Publication:
- United States
- Language:
- English
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