Enumeration-based Triangle Counting on GPUs

Abstract

Subgraph enumeration in partitioned graphs across distributed-memory systems is beset with challenges in balancing data movement with the local computation. Especially, counting the number of triangles induced by the closed wedges (i.e., length-3 cycles) is a measure of connectedness in a graph, but often limited by the significant search space caused by open wedges or length-2 paths (usually greater than the number of edges in a graph), which must be inspected to assess whether a particular wedge is closed. To mitigate triangle counting on massive graphs, distributed-memory partitioned-graph approaches are viable (i.e., assessing closed wedges independently within a partition), but load imbalance due to arbitrary communication can overshadow any gains from enhanced concurrency, owing to the inherent lack of structure in regular graphs. In this paper, we discuss a distributed-memory exact graph triangle counting implementation, and assess its performance over billion-edge real-world graphs on contemporary scale-out and scale-up based NVIDIA GPU platforms (considering NVIDIA ``Ampere'' and ``Hopper'' architectures), depicting a scalability spectrum of multiple orders of magnitude. Comparisons with existing state-of-the-art approaches demonstrates up to 10$\times$ improvements relative to distributed-memory CPU baseline, 2-100$\times$ over single-GPU vendor-optimized NVIDIA RAPIDS cuGraph and 10-60\% over multi-GPU $G^2$Miner, in terms of end-to-end execution times.