Proceedings of 37th Conference on Foundations of Computer Science (1996)

Burlington, VT

Oct. 14, 1996 to Oct. 16, 1996

ISBN: 0-8186-7594-2

pp: 462

M.R. Henzinffer , Syst. Res. Center, Digital Equipment Corp., Palo Alto, CA, USA

S. Rao , Syst. Res. Center, Digital Equipment Corp., Palo Alto, CA, USA

H.N. Gabow , Syst. Res. Center, Digital Equipment Corp., Palo Alto, CA, USA

ABSTRACT

The vertex connectivity /spl 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{/spl kappa//sup 3/+n,/spl kappa/n}m); for an undirected graph the term m can be replaced by /spl kappa/n. A randomized algorithm finds /spl 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(/spl kappa//sub 1/nmlog(n/sup 2//m)) where /spl kappa//sub 1//spl les/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 J. Hao and J.B. Orlin (1994) that computes edge connectivity.

INDEX TERMS

computational geometry; vertex connectivity; smallest number of vertices; deterministic algorithm; digraph; error probability; preflow push algorithm

CITATION

M. Henzinffer, H. Gabow and S. Rao, "Computing vertex connectivity: new bounds from old techniques,"

*Proceedings of 37th Conference on Foundations of Computer Science(FOCS)*, Burlington, VT, 1996, pp. 462.

doi:10.1109/SFCS.1996.548505

CITATIONS