On 2-Approximation to the Vertex-Connectivity in Graphs

Given a graph G, we give a fast algorithm for approximating the vertex connectivity κ of G. Our algorithm delivers a minimum vertex cut of G if κ <= δ/2 , and returns a message “κ > δ/2 ” otherwise, where δ denotes the minimum degree of G. The algorithm runs in O(n2(1+min{κ2, κ√n}/δ)) time and O(n+m) space, where n and m denote the numbers of vertices and edges in G, respectively. key words: graph algorithm, approximation algorithm, vertexconnectivity, MA orderings, minimum degree