A Simple Algorithm for Finding All k-Edge-Connected Components

The problem of finding k-edge-connected components is a fundamental problem in computer science. Given a graph G = (V, E), the problem is to partition the vertex set V into {V (1), V (2),…, V (h)}, where each V (i) is maximized, such that for any two vertices x and y in V (i), there are k edge-disjoint paths connecting them. In this paper, we present an algorithm to solve this problem for all k. The algorithm preprocesses the input graph to construct an Auxiliary Graph to store information concerning edge-connectivity among every vertex pair in O(Fn) time, where F is the time complexity to find the maximum flow between two vertices in graph G and n = ∣V∣. For any value of k, the k-edge-connected components can then be determined by traversing the auxiliary graph in O(n) time. The input graph can be a directed or undirected, simple graph or multigraph. Previous works on this problem mainly focus on fixed value of k.