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

TL;DR

This paper introduces a unified, scalable algorithm framework for temporal user-defined $(k, ext{X})$-core queries on dynamic graphs, enabling efficient analysis of various core metrics like size and interaction frequency.

Contribution

It extends previous temporal $k$-core queries by incorporating arbitrary metrics $ ext{X}$ within a two-phase framework, optimizing performance for diverse conditions.

Findings

Achieves state-of-the-art performance comparable to TCQ.

Supports a wide range of user-defined core metrics.

Reduces redundant computations through time zone concepts.

Abstract

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.