How can we enumerate triangles from an enormous graph with billions of vertices and edges? Triangle enumeration is an important task for graph data analysis with many applications including identifying suspicious users in social networks, detecting web spams, finding communities, etc. However, recent networks are so large that most of the previous algorithms fail to process them. Recently, several MapReduce algorithms have been proposed to address such large networks; however, they suffer from the massive shuffled data resulting in a very long processing time.

In this paper, we propose PTE (Pre-partitioned Triangle Enumeration), a new distributed algorithm for enumerating triangles in enormous graphs by resolving the structural inefficiency of the previous MapReduce algorithms. PTE enumerates trillions of triangles in a billion scale graph by decreasing three factors: the amount of shuffled data, total work, and network read. Experimental results show that PTE provides up to 47× faster performance than re-cent distributed algorithms on real world graphs, and succeeds in enumerating more than 3 trillion triangles on the ClueWeb12 graph with 6.3 billion vertices and 72 billion edges, which any previous triangle computation algorithm fail to process.