Temporal graphs are equipped with entities and the relationships between entities associated with time stamps. Cohesive subgraph mining (CSM) is a fundamental task in temporal graph analysis, which has gathered great research interests. It benefits from reflecting the dynamism of graphs and has many real-world applications. Yet, most existing work focus on the cohesive subgraph detection (CSD) problem, which identifies all the defined subgraphs in the entire temporal graphs. When graph size becoming too large, it is impractical. In this paper, we are the first to concern about the cohesive subgraph search (CSS) problem in large temporal graphs. In specific, given a query vertex, we are seeking the continual densely connected subgraph including the query vertex. To this end, (1) we model the cohesive subgraph in temporal graphs as a (𝜃,τ)-continual k-core and prove its NP-hardness; (2) we develop two exact algorithms based on different vertex enumeration strategies, called Exact-VD and Exact-VE, respectively. Exact-VD uses depth-first search to find the target subgraphs in a top-down way by gradually deleting vertices from the current subgraph; while Exact-VE starts from the query vertex and continuously expands the ranked vertices in the candidate group until reaching the target subgraphs. Meanwhile, several elegant pruning rules are designed to reduce the search space; (3) to further speed up, we propose an efficient approximate local search method, called Approx-LS, which greedily expands the current subgraph guided by the developed heuristic functions until identifying the results. Comprehensive experiments on four real-life datasets verify the efficiency and effectiveness of our proposed approaches.

时间图配备了实体以及与时间戳关联的实体之间的关系。内聚子图挖掘（CSM）是时态图分析中的一项基本任务，引起了人们极大的研究兴趣。它受益于反映图形的动态性，并具有许多实际应用。然而，大多数现有工作都集中在内聚子图检测（CSD）问题上，该问题在整个时间图中识别所有定义的子图。当图尺寸变得太大时，这是不切实际的。在本文中，我们是第一个关注大时间图中的内聚子图搜索（CSS）问题的人。具体来说，给定一个查询顶点，我们正在寻找包括查询顶点的连续密集连接子图。为此，（1）我们将时间图中的内聚子图建模为（𝜃 , τ )-连续k核并证明其 NP 硬度；(2) 我们开发了两种基于不同顶点枚举策略的精确算法，分别称为Exact-VD和Exact-VE。Exact-VD使用深度优先搜索，通过从当前子图中逐渐删除顶点，以自顶向下的方式找到目标子图；而Exact-VE从查询顶点开始，不断扩展候选组中的排序顶点，直到到达目标子图。同时，设计了几个优雅的剪枝规则来减少搜索空间；(3) 为了进一步加快速度，我们提出了一种有效的近似局部搜索方法，称为Approx-LS，它会贪婪地扩展由开发的启发式函数引导的当前子图，直到识别出结果。对四个真实数据集的综合实验验证了我们提出的方法的效率和有效性。