An Effective Algorithm for Extracting Maximal Bipartite Cliques

Abstract

The reduction of bipartite clique enumeration problem into a clique enumeration problem is a well-known approach for extracting maximal bipartite cliques. In this approach, the graph inflation is used to transform a bipartite graph to a general graph, then any maximal clique enumeration algorithm can be used. However, between every two vertices (in the same set), the traditional inflation algorithm adds a new edge. Therefore incurring high computation overhead, which is impractical and cannot be scaled up to handle large graphs. This paper proposes a new algorithm for extracting maximal bipartite cliques based on an efficient graph inflation algorithm. The proposed algorithm adds the minimal number of edges that are required to convert all maximal bipartite cliques to maximal cliques. The proposed algorithm has been evaluated, using different real world benchmark graphs, according to the correctness of the algorithm, running time (in the inflation and enumeration steps), and according to the overhead of the inflation algorithm on the size of the generated general graph. The empirical evaluation proves that the proposed algorithm is accurate, efficient, effective, and applicable to real world graphs more than the traditional algorithm.