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.N. Gabow, "Using expander graphs to find vertex connectivity", FOCS, 2000, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2000, pp. 410, doi:10.1109/SFCS.2000.892129