A Unified and Scalable Algorithm Framework of User-Defined Temporal (k,X)-Core Query
Ming Zhong, Junyong Yang, Yuanyuan Zhu, Tieyun Qian, Mengchi Liu, Jeffrey Xu Yu · IEEE Transactions on Knowledge and Data Engineering · 2024
Querying cohesive subgraphs on temporal graphs (e.g., social network, finance network, etc.) with various conditions has attracted intensive research interests recently. In this paper, we study a novel Temporal$(k,\mathcal {X})$-Core Query (TXCQ) that extends a fundamental Temporal$k$-Core Query (TCQ) proposed in our conference paper by optimizing or constraining an arbitrary metric$\mathcal {X}$of$k$-core, such as size, engagement, interaction frequency, time span, burstiness, periodicity, etc. Our objective is to address specific TXCQ instances with conditions on different$\mathcal {X}$in a unified algorithm framework that guarantees scalability. For that, this journal paper proposes a taxonomy of measurement$\mathcal {X}(\cdot )$and achieve our objective using a two-phase framework while$\mathcal {X}(\cdot )$is time-insensitive or time-monotonic. Specifically, Phase 1 still leverages the query processing algorithm of TCQ to induce all distinct$k$-cores during a given time range, and meanwhile locates the “time zones” in which the cores emerge. Then, Phase 2 conducts fast local search and$\mathcal {X}$evaluation in each time zone with respect to the time insensitivity or monotonicity of$\mathcal {X}(\cdot )$. By revealing two insightful concepts named tightest time interval and loosest time interval that bound time zones, the redundant core induction and unnecessary$\mathcal {X}$evaluation in a zone can be reduced dramatically. Our experimental results demonstrate that TXCQ can be addressed as efficiently as TCQ, which achieves the latest state-of-the-art performance, by using a general algorithm framework that leaves$\mathcal {X}(\cdot )$as a user-defined function.