Finding a Summary for All Maximal Bicliques

The number of bicliques in a bipartite graph may grow exponentially as its vertices increase. A biclique summary is a subset of all maximal bicliques and can somehow represent all maximal bicliques. In practical application scenarios, a summary helps users obtain more representative results. Due to its compact size, it enables users to efficiently locate and select the information they need. For instance, in the biomedical field, when researchers explore relationships between genes and proteins, they are often faced with an excessive number of combinations. Using a summary of these gene-protein relationships not only provides more representative insights but also significantly reduces the time needed for analysis. To find such representative maximal bicliques faster, we propose a method to determine whether to terminate the current search by computing lower bounds. We begin by introducing a baseline method, MBS, followed by two algorithms that incorporate bound pruning: MBSL, a neighborhood-based search algorithm, and MBSc, an$(\alpha,\beta)$- core-based search algorithm. We also provide three strategies for optimizing the algorithms. They are the Upper Bound Deflation Pruning method, the Intersection Deflation Heuristic method, and the Lazy Lower Bound Evaluation method. Based on the above optimization strategies, we present the advanced algorithms MBSA and MBScA. In experiments, we demonstrate the efficiency and result quality of the proposed algorithms. After incorporating three optimization strategies, MBSA and MBScA show improvements in computation time compared to the baseline MBS and are able to generate smaller summaries.