Querying Historical Cohesive Subgraphs Over Temporal Bipartite Graphs

In many real-world scenarios, relationships between two different entities can be naturally represented as bipartite graphs, such as author-paper, user-item, and people-location. Cohesive subgraph search, which aims to find densely connected subgraphs, is a popular research topic on bipartite graphs. While various cohesive subgraph models are proposed on bipartite graphs, none of them consider the temporal dimension, which expresses dynamic changes occurring in cohesive subgraphs over time. In this paper, we propose the first cohesive subgraph model$(\alpha,\ \beta,\ \mathcal{T})$-core on temporal bipartite graphs. Given degree constraints$\alpha$and$\beta$, as well as a time window$\mathcal{T}=[t_{s},t_{e}],(\alpha,\beta,\ \mathcal{T})$-core guarantees that each vertex in the upper or lower layer has at least$\alpha$or$\beta$neighbors, respectively, within the snapshot over the time window$\mathcal{T}$. An intuitive solution to compute the$(\alpha,\ \beta,\ \mathcal{T})$-core is to iteratively remove the vertices that do not satisfy the degree constraints in the snapshot, which suffers from inefficiency and is impractical on large temporal bipartite graphs. Therefore, we turn to index-based methods to enhance query performance. To support efficient arbitrary$(\alpha,\ \beta,\ \mathcal{T})$-core queries, we propose a vertex-partitioning historical index called VH-Index and a time-partitioning historical index called TH-Index. Note that these two indexes need to store$(\alpha,\ \beta,\ \mathcal{T})$-core for each possible combination of$\alpha, \beta$, and$a\mathcal{T}$and incur large construction costs. Therefore, we further propose a temporal intersection index called TH*-Index to strike a balance between the efficiency of query processing and the space cost of the index. We develop both sequential and parallel algorithms for efficiently constructing the temporal-intersection index. Extensive experiments are conducted on 10 real-world temporal bipartite graphs to validate the effectiveness of the$(\alpha,\ \beta,\ \mathcal{T})$-core model and the efficiency of our proposed algorithms.