Labeled Triangle Indexing for Efficiency Gains in Distributed Interactive Subgraph Search††This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-CONF-814976). Experiments were performed at the Livermore Computing facility.

TLDR: In this paper, the authors propose to decompose a search pattern into a set of constraints, and use each of these constraints to eliminate non-matching vertices and edges.

Abstract: Subgraph search in a massive background graph, i.e., pattern matching in graphs, is a challenging problem, particularly in an interactive usage scenario where fast response time is important. Our approach, Prune.Juice [1], is based on two intuitions: first, rather than directly searching for individual matches, it is cheaper to eliminate vertices and edges of the background graph that do not participate in any match. Second, to perform this pruning process, it is possible to decompose a search pattern into a set of constraints, and use each of these constraints to eliminate non-matching vertices and edges. This paper explores the feasibility of indexing the background graph to accelerate the checking of non-local constraints (e.g., cycles and paths), the most expensive phase of pruning. In particular, we demonstrate that indexing labeled triangle (i.e., a 3-Cycle) participation is a valuable acceleration technique. Additionally, we observe that labeled triangle counts at edges can be employed to detect 3-Paths that have terminal points with non-unique labels, at relatively little extra cost. Such paths and triangles are basic sub-constraints that can be used to rapidly prune non-matching vertices and edges. As proof of concept, we show that, using triangle information alone, indexing further accelerates expensive queries in Prune.Juice by up to $\mathbf{500}\times$ on billion-edge graphs.