Hop-Constrained s-t Simple Path Enumeration in Billion-Scale Labelled Graphs

Abstract

Hop-constrained s-t simple path (${\textsf{HC}}\text {-}{\textsf{s}}\text {-}{\mathsf {t~path}}$) enumeration is a fundamental problem in graph analysis. Existing solutions for this problem focus on unlabelled graphs and assume queries are issued without any label constraints. However, in many real-world applications, graphs are edge-labelled and the queries involve label constraints on the path connecting two vertices. Therefore, we study the problem of labelled hop-constrained s-t path ($\textsf{LHC}$-$\textsf{s}$-$\mathsf {t~path}$) enumeration in this paper. We aim to efficiently enumerate the $\textsf{HC}$-$\textsf{s}$-$\mathsf {t~paths}$ using only edges with provided labels. To achieve this goal, we first demonstrate the existence of unnecessary computation specific to the label constraints in the state-of-the-art $\textsf{HC}$-$\textsf{s}$-$\mathsf {t~path}$ enumeration algorithm. We then devise a novel online index to identify the fruitless exploration during the enumeration. Based on the proposed index, we design an efficient $\textsf{LHC}$-$\textsf{s}$-$\mathsf {t~path}$ enumeration algorithm in which unnecessary computation is effectively pruned. Extensive experiments are conducted on real-world graphs with billions of edges. Experiment results show that our proposed algorithms significantly outperform the baseline methods by over one order of magnitude.