Fast In-Memory Triangle Listing for Large Real-World Graphs.

ABSTRACTTriangle listing, or identifying all the triangles in an undirected graph, is a very important graph problem that serves as a building block of many other graph algorithms. The compute-intensive nature of the problem, however, necessitates an efficient method to solve this problem, especially for large real-world graphs. In this paper we propose a fast and precise in-memory solution for the triangle listing problem. Our solution includes fast common neighborhoods finding methods that consider power law degree distribution of real-word graphs. We prove how theoretic lower bound can be achieved by sorting the nodes in the graph by their degree and applying pruning. We explain how our techniques can be applied automatically by an optimizing DSL compiler. Our experiments show that hundreds of billions of triangles in a five billion edge graph can be enumerated in about a minute with a single server-class machine.