Querying Cohesive Subgraph regarding Span-Constrained Triangles on Temporal Graphs with Dynamic Index Maintenance

2026-06-09

AI Summary

This work addresses the challenge of querying subgraphs in temporal graphs that simultaneously exhibit static structural cohesiveness and adhere to temporal window constraints. The paper introduces, for the first time, the (k,δ)-truss model to uniformly characterize triangle-dense subgraphs within bounded time spans. To support efficient query processing, the authors design a highly compressible index structure amenable to dynamic maintenance. This index leverages truss decomposition and dual containment relationships to achieve lossless compression, while organizing data via tree- or map-based structures to enable incremental updates. Experimental results demonstrate that the proposed approach accelerates query execution by two to four orders of magnitude compared to non-indexed baselines, achieves a compression ratio as low as 10⁻⁴, and supports both interactive-time query responses and efficient index updates.

Abstract

Recent advances in temporal graph research have redefined traditional static graph concepts such as triangles, motifs, and $k$-cores. Inspired by this, we introduce a novel $(k,δ)$-truss for temporal graphs, requiring triangles to exist within sufficiently short time windows. The $(k,δ)$-truss ensures both static and temporal cohesion, while the original $k$-truss is a special case when $δ= \infty$. To address $(k,δ)$-truss queries, we propose index-free and index-based approaches. Utilizing the dual containment relation of $(k,δ)$-trusses, our indexes losslessly compress all $(k,δ)$-trusses into map or tree structures, significantly reducing space while enabling optimal-time retrieval. To scale to large temporal graphs, we develop two index construction algorithms based on truss decomposition and truss maintenance, respectively, which substantially reduce redundant computations. Moreover, we present techniques for the dynamic maintenance of the proposed indexes. The experimental results demonstrate that index-based approaches process queries in interactive time and outperform the index-free approach by 2$\sim$4 orders of magnitude, while the indexes achieve compression ratios of up to $10^{-4}$ and can be updated efficiently without rebuilding from scratch.

Problem

• temporal graphs
• cohesive subgraph
• span-constrained triangles
• dynamic index maintenance
• truss

Innovation

• temporal graph
• k-truss
• span-constrained triangle
• dynamic index maintenance
• cohesive subgraph