BCviz: A Linear-Space Index for Mining and Visualizing Cohesive Bipartite Subgraphs

Finding the maximum biclique in a bipartite graph is a fundamental graph analysis problem. Existing methods for maximum biclique search are not very efficient because they cannot effectively reduce the size of a bipartite graph composed of large bicliques that are loosely linked together because the graph reduction strategies adopted by these methods only consider local densities of vertices. This paper proposes a novel approach to maximum biclique search. The unique feature of this approach is building a linear-space data-driven index called BCviz that helps accurately identify subgraphs containing all bicliques with sizes no less than a certain threshold. The core technique of BCviz is determining a total order of vertices that can reveal both the local density and the connectivity of the vertices. Notably, our work is the first one to take connectivity into account in graph reduction. Interestingly, the total order of vertices entails BCviz an illustrative visualization of the distribution of cohesive subgraphs in the input graph. To deeply understand BCviz, we carry out a theoretical study on its properties and reveal how it enables more effective graph reduction. Based on BCviz, we propose an exact maximum biclique search algorithm that searches for results on much smaller subgraphs than any existing method does. In addition, we improve the efficiency of index construction by two techniques. One is approximating an edge's local density with an upper bound that can be derived in linear time. The other is a lightweight vertex ordering method called one-spot ordering which reduces unnecessary cohesion computations. Extensive experiments indicate that the proposed maximum biclique search methods based on BCviz and its variants outperform the state-of-the-art search-based methods by 2--3 orders of magnitude. Compared with the state-of-the-art index for maximum biclique search, the improved BCviz index can reduce the index size by 1--2 orders of magnitude and the index construction time by up to 2 orders of magnitude.