Querying Cohesive Subgraph Regarding Span-Constrained Triangles on Temporal Graphs

The recent prosperity of temporal graph research redefines many traditional concepts on static graphs, such as triangle, motif,
$k$
-core, etc. Inspired by that, we propose a novel
$(k, \delta)$
-truss on temporal graphs, which requires its triangles to exist in short enough time windows ever. The
$(k,\delta)$
-truss satisfies both static and temporal cohesion, while the original
$k$
-truss is its special case when
$\delta=\infty$
. In order to address the
$(k, \delta)$
-truss query, we propose both index-free and index-based approaches. By leveraging the dual containment relation on
$(k, \delta)$
-trusses, our indexes can compress all
$(k, \delta)$
-trusses losslessly into map or tree structures with dramatically less space, so that a specific
$(k,\ \delta)$
-truss can be retrieved from indexes in the optimal time. To enable our index to scale to large temporal graphs, we develop two index construction algorithms that can reduce redundant computation significantly, based on truss decomposition and truss maintenance respectively. The experimental results demonstrate that index-based approaches process queries in interactive time and outperform the index-free approach by 2~4 orders of magnitude, while indexes achieve compression ratios up to 10-
⁴
.