Finding Maximum Edge Biclique in Bipartite Networks by Integer Programming

Abstract

The problem of finding bicliques in graphs arises in areas such as bioinformatics, social networks, citation networks and data mining. Most of the algorithms that appear in the literature are based on enumeration of bicliques. We may have an exponential number of bicliques in a graph. Maximum edge biclique problem is NP-complete. When looking for a maximum edge biclique on large graph, enumeration based algorithms may be subject to an explosive number of enumerated bicliques. Even though there are very efficient enumeration based solver packages around, there is also a need for a solver that can just report a single maximum edge biclique. We contribute an integer programming based algorithm for finding the maximum edge biclique on bipartite graphs. Our algorithm called BIIP, makes use of quaternary search and other optimizations to locate an optimal solution by making calls to an integer programming solver. We provide timing results of our solver on graphs coming from the bioinformatics field. Our BIIP solver is available at https://github.com/melihsozdinler/biip.