Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)
Redondo Beach, California
Nov. 12, 2000 to Nov. 14, 2000
H.N. Gabow , Dept. of Comput. Sci., Colorado Univ., Boulder, CO, USA
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 algorithm for finding /spl kappa/. For a digraph with n vertices, m edges and connectivity /spl kappa/ the time bound is O((n+min(/spl kappa//sup 5/2/,/spl kappa/n/sup 3/4/))m). This improves the previous best bound of O((n+min(/spl kappa//sup 3/,/spl kappa/n))m). For an undirected graph both of these bounds hold with m replaced /spl kappa/n. Our approach uses expander graphs to exploit nesting properties of certain separation triples.
graph theory; computational complexity; expander graphs; vertex connectivity; digraph; time bound; undirected graph; nesting properties; separation triples; complexity
H. Gabow, "Using expander graphs to find vertex connectivity," Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS), Redondo Beach, California, 2000, pp. 410.