A Unified and Scalable Algorithm Framework of User-Defined Temporal $(k,\mathcal {X})$(k,X)-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
$(k,\mathcal {X})$
-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.