PDTL: Parallel and Distributed Triangle Listing for Massive Graphs

This paper presents the first distributed triangle listing algorithm with provable CPU, I/O, Memory, and Network bounds. Finding all triangles (3-cliques) in a graph has numerous applications for density and connectivity metrics, but the majority of existing algorithms for massive graphs are sequential, while distributed versions of algorithms do not guarantee their CPU, I/O, Memory, or Network requirements. Our Parallel and Distributed Triangle Listing (PDTL) framework focuses on efficient external-memory access in distributed environments instead of fitting sub graphs into memory. It works by performing efficient orientation and load-balancing steps, and replicating graphs across machines by using an extended version of Hu et al.'s Massive Graph Triangulation algorithm. PDTL suits a variety of computational environments, from single-core machines to high-end clusters, and computes the exact triangle count on graphs of over 6B edges and 1B vertices (e.g. Yahoo graphs), outperforming and using fewer resources than the state-of-the-art systems Power Graph, OPT, and PATRIC by 2x to 4x. Our approach thus highlights the importance of I/O in a distributed environment.