Cohesive subgraph mining is a fundamental problem in bipartite graph analysis. In reality, relationships between two types of entities often occur at some specific timestamps, which can be modeled as a temporal bipartite graph. However, the temporal information is widely neglected by previous studies. Moreover, directly extending the existing models may fail to find some critical groups in temporal bipartite graphs, which appear in a unilateral (i.e., one-layer) form. To fill the gap, in this paper, we propose a novel model, called maximal \lambda-frequency group (MFG). Given a temporal bipartite graph G=(U,V,E), a vertex set V_S \subseteq V is an MFG if i) there are no less than \lambda timestamps, at each of which V_S can form a (t_U,t_V)-biclique with some vertices in U at the corresponding snapshot, and ii) it is maximal. To solve the problem, a filter-and-verification (FilterV) method is proposed based on the Bron-Kerbosch framework, incorporating novel filtering techniques to reduce the search space and array-based strategy to accelerate the frequency and maximality verification. Nevertheless, the cost of frequency verification in each valid candidate set computation and maximality check could limit the scalability of FilterV to larger graphs. Therefore, we further develop a novel verification-free (VFree) approach by leveraging the advanced dynamic counting structure proposed. Theoretically, we prove that VFree can reduce the cost of each valid candidate set computation in FilterV by a factor of O(|V|). Furthermore, VFree can avoid the explicit maximality verification because of the developed search paradigm. Finally, comprehensive experiments on 15 real-world graphs are conducted to demonstrate the efficiency and effectiveness of the proposed techniques and model.

翻译：凝聚子图挖掘是二分图分析中的一个基本问题。现实中，两类实体之间的关系常发生于特定时间戳，可建模为时序二分图。然而，现有研究普遍忽视时序信息。此外，直接扩展现有模型可能无法发现时序二分图中以单侧（即单层）形式出现的关键群组。为填补这一空白，本文提出一种称为最大λ-频率群组（MFG）的新模型。给定时序二分图G=(U,V,E)，顶点集V_S ⊆ V是一个MFG当且仅当：i) 存在不少于λ个时间戳，在每个对应快照中V_S能与U中的某些顶点形成(t_U,t_V)-双团；ii) 该集合是极大的。为解决该问题，我们基于Bron-Kerbosch框架提出过滤-验证（FilterV）方法，通过引入新型过滤技术缩减搜索空间，并采用基于数组的策略加速频率与极大性验证。然而，每个有效候选集计算中的频率验证和极大性检查成本可能限制FilterV在大规模图上的可扩展性。为此，我们进一步利用提出的先进动态计数结构，开发了无需验证（VFree）的新方法。理论上，我们证明VFree能将FilterV中每个有效候选集计算成本降低O(|V|)倍。此外，得益于开发的搜索范式，VFree可避免显式的极大性验证。最后，通过在15个真实图数据集上的综合实验，验证了所提技术与模型的高效性和有效性。