A Unified and Scalable Algorithm Framework of User-Defined Temporal (k, χ)-Core Query

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,chi)-Core Query (TXCQ) that extends a fundamental Temporal k-Core Query (TCQ) proposed in our conference paper by optimizing or constraining an arbitrary metric chi 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 X in a unified algorithm framework that guarantees scalability. For that, this journal paper proposes a taxonomy of measurement chi(<middle dot>) and achieve our objective using a two-phase framework while chi(<middle dot>) 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 chi evaluation in each time zone with respect to the time insensitivity or monotonicity of chi(<middle dot>). By revealing two insightful concepts named tightest time interval and loosest time interval that bound time zones, the redundant core induction and unnecessary chi 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 chi(<middle dot>) as a user-defined function.