Accelerating Set Intersections over Graphs by Reducing-Merging

Given two sets of vertices Sa and Sb 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. Thus, accelerating set intersections is beneficial to these algorithms. In the paper, we propose a novel reducing-merging framework for 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 using the classic merging algorithm. To optimize the range codes that sketch the vertices, we formulate the problem of range code optimization and prove its NP-hardness. We develop efficient yet effective algorithms for two typical scenarios global intersection and local intersection. Moreover, we present a novel two-level merging algorithm to enhance the performance. The results of extensive experiments over real graphs show that our approach can achieve significant speedups compared to the merge-based algorithm.