Novel Algorithm to Find Maximum Clique

Abstract

In maximum clique problem is to find largest sub-graph of a graph in which, any two vertices are adjacent. The maximum clique problem falls into category of NP-hard problems. It is, therefore, often avoided to detect maximum clique by practitioners in many applications despite the fact that it has significant applications in the field of information retrieval, data mining, network analysis etc. Community Detection in social networks is one of the recent trends in computer science. Maximum Clique and community in social networks have overlapping definitions in respective domains. Thus problem of community detection in social networks reduces to finding cliques in graphs, provided social networks are represented as graphs. Several exact algorithms to find maximum clique already exist in literature that promise acceptable runtimes on certain graphs. But problem arises when these algorithms are applied on real world graphs which are massive in size. In this work, a novel branch and bound exact algorithm, to find maximum clique, has been presented with new pruning steps. This algorithm has been tested on real world graphs and DIMACS benchmark graphs, where it exhibits runtimes several times better than other existing algorithms and it performs notably well on large sparse real world graphs.