Linear algebraic primitives for parallel computing on large graphs

• Authors: John R. Gilbert;Aydin Buluc
• Venue: Linear algebraic primitives for parallel computing on large graphs
• Year: 2010

This dissertation presents a scalable high-performance software library to be used for graph analysis and data mining. Large combinatorial graphs appear in many applications of high-performance computing, including computational biology, informatics, analytics, web search, dynamical systems, and sparse matrix methods.Graph computations are difficult to parallelize using traditional approaches due to their irregular nature and low operational intensity. Many graph computations, however, contain sufficient coarse grained parallelism for thousands of processors that can be uncovered by using the right primitives. We will describe the Parallel Combinatorial BLAS, which consists of a small but powerful set of linear algebra primitives specifically targeting graph and data mining applications. Given a set of sparse matrix primitives, our approach to developing a library consists of three steps. We (1) design scalable parallel algorithms for the key primitives, analyze their performance, and implement them on distributed memory machines, (2) develop reusable software and evaluate its performance, and finally (3) perform pilot studies on emerging architectures. The technical heart of this thesis is the development of a scalable sparse (generalized) matrix-matrix multiplication algorithm, which we use extensively as a primitive operation for many graph algorithms such as betweenness centrality, graph clustering, graph contraction, and subgraph extraction. We show that 2D algorithms scale better than 1D algorithms for sparse matrix-matrix multiplication. Our 2D algorithms perform well in theory and in practice.