PMV: Pre-partitioned Generalized Matrix-Vector Multiplication for Scalable Graph Mining

Abstract: How can we analyze enormous networks including the Web and social networks which have hundreds of billions of nodes and edges? Network analyses have been conducted by various graph mining methods including shortest path computation, PageRank, connected component computation, random walk with restart, etc. These graph mining methods can be expressed as generalized matrix-vector multiplication which consists of few operations inspired by typical matrix-vector multiplication. Recently, several graph processing systems based on matrix-vector multiplication or their own primitives have been proposed to deal with large graphs; however, they all have failed on Web-scale graphs due to insufficient memory space or the lack of consideration for I/O costs. In this paper, we propose PMV (Pre-partitioned generalized Matrix-Vector multiplication), a scalable distributed graph mining method based on generalized matrix-vector multiplication on distributed systems. PMV significantly decreases the communication cost, which is the main bottleneck of distributed systems, by partitioning the input graph in advance and judiciously applying execution strategies based on the density of the pre-partitioned sub-matrices. Experiments show that PMV succeeds in processing up to 16x larger graphs than existing distributed memory-based graph mining methods, and requires 9x less time than previous disk-based graph mining methods by reducing I/O costs significantly.