A powerful reducing framework for accelerating set intersections over graphs

Zheng Hu, Cong Xu, Weiguo Zheng

Abstract: Given two sets of vertices \(S_a\) and \(S_b\) of a graph, computing their common vertices, namely set intersection, is one primitive operation in many graph algorithms such as triangle counting, maximal clique enumeration, and subgraph matching. Therefore, accelerating set intersections is beneficial to these graph tasks. In the paper, we propose a novel reducing framework for speeding up set intersections over graphs rather than intersecting the two sets directly. In the reducing phase, the vertices that cannot fall into the intersection are screened out by applying the range reduction. Based on the truncated subsets, the intersection can be easily obtained at low cost. To optimize the range codes, we formulate the problem of range code optimization and prove its NP-hardness. We develop efficient yet effective algorithms for two typical scenarios, namely global intersection and local intersection. Moreover, we present a novel two-level strategy and a nested reducing framework to enhance the performance. The results of extensive experiments over real graphs show that our approach can achieve significant speedups compared to the state-of-the-art algorithms.