Efficient k-edge connected component detection through an early merging and splitting strategy

Abstract

Computing k-edge connected components can be used to capture closely related vertices in a graph. It is an important problem with many applications. Due to the high time complexities of traditional algorithms for computing k-edge connected components, it is difficult for them to be applied to efficiently process large scale graphs. In this paper, an early merging and splitting based maximal k-edge connected subgraph detection algorithm, named MSK, is proposed. It computes the k-edge connected components of a graph with an order list of vertices which is decided according to the connectivity of vertices in the graph. During the processing of the vertex list, if two vertices are k-edge connected, they are merged into a super-vertex. On the contrary , if the vertex pair does not satisfy the condition of k-edge connectivity, the related vertices and edges are removed from the graph, and the graph is decomposed into several subgraphs. The above steps are performed iteratively in the obtained subgraphs until each subgraph become a k-edge connected component. In order to further improve the time efficiency, an approximate algorithm PMSK is also proposed. The experimental results on a large number of real and synthetic graphs show that the proposed algorithms are accurate and more efficient than the state-of-the-art algorithms.