New Algorithms for Enumerating All Maximal Cliques

In this paper, we consider the problems of generating all maximal (bipartite) cliques in a given (bipartite) graph G = (V, E) with n vertices and m edges. We propose two algorithms for enumerating all maximal cliques. One runs with O(M(n)) time delay and in O(n2 ) space and the other runs with O(∆4 ) time delay and in O(n + m) space, where ∆ denotes the maximum degree of G, M(n) denotes the time needed to multiply two n × n matrices, and the latter one requires O(nm) time as a preprocessing. For a given bipartite graph G, we propose three algorithms for enumerating all maximal bipartite cliques. The first algorithm runs with O(M(n)) time delay and in O(n2 ) space, which immediately follows from the algorithm for the nonbipartite case. The second one runs with O(∆3 ) time delay and in O(n + m) space, and the last one runs with O(∆2 ) time delay and in O(n + m + N∆) space, where N denotes the number of all maximal bipartite cliques in G and both algorithms require O(nm) time ...

• Type: Conference
• Year: 2004
• Where: SWAT
• Authors: Kazuhisa Makino, Takeaki Uno
• Keywords: Algorithms, Maximal Bipartite Cliques, SWAT 2004, Time Delay