Topology-aware optimization of big sparse matrices and matrix multiplications on main-memory systems

Since data sizes of analytical applications are continuously growing, many data scientists are switching from customized micro-solutions to scalable alternatives, such as statistical and scientific databases. However, many algorithms in data mining and science are expressed in terms of linear algebra, which is barely supported by major database vendors and big data solutions. On the other side, conventional linear algebra algorithms and legacy matrix representations are often not suitable for very large matrices. We propose a strategy for large matrix processing on modern multicore systems that is based on a novel, adaptive tile matrix representation (AT MATRIX). Our solution utilizes multiple techniques inspired from database technology, such as multidimensional data partitioning, cardinality estimation, indexing, dynamic rewrites, and many more in order to optimize the execution time. Based thereon we present a matrix multiplication operator ATMULT, which outperforms alternative approaches. The aim of our solution is to overcome the burden for data scientists of selecting appropriate algorithms and matrix storage representations. We evaluated AT MATRIX together with ATMULT on several real-world and synthetic random matrices

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the optimizations and techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph-Based Benchmark Suite (GBBS).Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201