Enumerating Maximal Bicliques from a Large Graph Using MapReduce

We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many data mining problems arising in social network analysis and bioinformatics. We present novel parallel algorithms for the MapReduce framework, and an experimental evaluation using Hadoop MapReduce. Our algorithm is based on clustering the input graph into smaller subgraphs, followed by processing different subgraphs in parallel. Our algorithm uses two ideas that enable it to scale to large graphs: (1) the redundancy in work between different subgraph explorations is minimized through a careful pruning of the search space, and (2) the load on different reducers is balanced through a task assignment that is based on an appropriate total order among the vertices. We show theoretically that our algorithm is work optimal, i.e., it performs the same total work as its sequential counterpart. We present a detailed evaluation which shows that the algorithm scales to large graphs with millions of edges and tens of millions of maximal bicliques. To our knowledge, this is the first work on maximal biclique enumeration for graphs of this scale.