H-INDEX: Hash-Indexing for Parallel Triangle Counting on GPUs

Abstract

Triangle counting is a graph algorithm that calculates the number of triangles involving each vertex in a graph. Briefly, a triangle encompasses three vertices from a graph, where every vertex possesses at least one incidental edge to the other two vertices from the triangle. Consequently, list intersection, which identifies the incidental edges, becomes the core algorithm for triangle counting. At the meantime, attracted by the enormous parallel computing potential of Graphics Processing Units (GPUs), numerous efforts have been devoted to deploy triangle counting algorithms on GPUs.While state-of-the-art intersection algorithms, such as merge-path and binary-search, perform well on traditional multi-core CPU systems, deploying them on massively parallel GPUs turns out to be challenging. In particular, merge-path based approach experiences the hardship of evenly distributing the workload across vast GPU threads and irregular memory accesses. Binary-search based approach often suffers from the potential problem of high time complexity. Furthermore, both approaches require sorted neighbor lists from the input graphs, which involves nontrivial preprocessing overhead. To this end, we introduce H-INDEX, a hash-indexing assisted triangle counting algorithm that overcomes all the aforementioned shortcomings. Notably, HINDEX achieves 141.399 billion TEPS computing rate on a Protein K-mer V2a graph with 64 GPUs. To the best of our knowledge, this is the first work that advances triangle counting beyond the 100 billion TEPS rate.