Fast Algorithms for the Maximum Clique Problem on Massive Graphs with Applications to Overlapping Community Detection

Bharath Pattabiraman, Md. Mostofa Ali Patwary, Assefaw H. Gebremedhin, Wei-keng Liao, Alok Choudhary
2015 Internet Mathematics  
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, information retrieval and many other areas related to the World Wide Web. There exist several algorithms for the problem with acceptable runtimes for certain classes of graphs, but many of them are infeasible for massive graphs. We present a new exact algorithm that employs novel pruning techniques and is able to find maximum cliques in very large, sparse graphs quickly. Extensive
more » ... iments on different kinds of synthetic and real-world graphs show that our new algorithm can be orders of magnitude faster than existing algorithms. We also present a heuristic that runs orders of magnitude faster than the exact algorithm while providing optimal or near-optimal solutions. We illustrate a simple application of the algorithms in developing methods for detection of overlapping communities in networks.
doi:10.1080/15427951.2014.986778 fatcat:wvwcxxvgjveh5l3hb7xnxq6q6q