The complete subgraphs of a bipartite graph are called bicliques. The cohesive structure has many applications such as review summary, biological study, and community discovery. Maximal biclique enumeration is a fundamental problem that has been widely studied. Unfortunately, research on this problem has been limited to static bipartite graphs. To keep coincident with reality better, we introduce this problem into temporal bipartite graphs. Based on this, we propose the concept of \(\Delta \) -biclique and the problem of maximal \(\Delta \) -biclique enumeration. To address this problem, we propose a baseline solution named MTBEA and an optimization technique named batch update technique. Given an unweighted and undirected temporal bipartite graph \(G=(L, R, E, \mathcal {T})\) and a positive integer parameter \(\Delta \) , we aim to find all maximal \(\Delta \) -bicliques of G. In any subinterval of length \(\Delta \) within interval \(T=[b,e]\) , a \(\Delta \) -biclique \(B=(P \subseteq L, Q \subseteq R, T)\) is always the same static complete subgraph. There are two easy solutions to our problem, which are the brute-force and greedy-based solutions. Both solutions require a significant amount of memory space. However, MTBEA outperforms them in terms of both time and space consumption. Although MTBEA presents an effective framework to our problem, it is not adept at handling edges that appear at the same timestamp. To further enhance the performance of MTBEA, we propose the optimization technique, batch update technique, which has two effects: an expanding effect and a pruning effect. The expanding effect accelerates the enumeration process by expanding a batch of vertices, while the pruning effect works by skipping a batch of search spaces. The experimental results demonstrate the efficiency of MTBEA and batch update technique.
