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This paper presents the first hybrid MPI+OpenMP+CUDA implementation of a distributed memory right-looking unsymmetric sparse direct solver (i.e., sparse LU factorization) that uses static pivoting. While BLAS calls can account for more than 40% of the overall factorization time, the difficulty is that small problem sizes dominate the workload, making efficient GPU utilization challenging. This fact motivates our approach, which is to find ways to aggregate collections of small BLAS operations into larger ones; to schedule operations to achieve load balance and hide long-latency operations, such as PCIe transfer; and to exploit simultaneously all of a node's available CPU cores and GPUs.

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Kernel summations are a ubiquitous key computational bottleneck in many data analysis methods. In this paper, we attempt to marry, for the first time, the best relevant techniques in parallel computing, where kernel summations are in low dimensions, with the best general‐dimension algorithms from the machine learning literature. We provide the first distributed implementation of kernel summation framework that can utilize: (i) various types of deterministic and probabilistic approximations that may be suitable for low and high‐dimensional problems with a large number of data points; (ii) any multidimensional binary tree using both distributed memory and shared memory parallelism; and (iii) a dynamic load balancing scheme to adjust work imbalances during the computation. Our hybrid message passing interface (MPI)/OpenMP codebase has wide applicability in providing a general framework to accelerate the computation of many popular machine learning methods. Our experiments show scalability results for kernel density estimation on a synthetic ten‐dimensional dataset containing over one billion points and a subset of the Sloan Digital Sky Survey Data up to 6144 cores. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2013

Due to the limited capacity of GPU memory, the majority of prior work on graph applications on GPUs has been restricted to graphs of modest sizes that fit in memory. Recent hardware and software advances make it possible to address much larger host memory transparently as a part of a feature known as unified virtual memory. While accessing host memory over an interconnect is understandably slower, the problem space has not been sufficiently explored in the context of a challenging workload with low computational intensity and an irregular data access pattern such as graph traversal. We analyse the performance of breadth first search (BFS) for several large graphs in the context of unified memory and identify the key factors that contribute to slowdowns. Next, we propose a lightweight offline graph reordering algorithm, HALO (Harmonic Locality Ordering), that can be used as a pre-processing step for static graphs. HALO yields speedups of 1.5x-1.9x over baseline in subsequent traversals. Our method specifically aims to cover large directed real world graphs in addition to undirected graphs whereas prior methods only account for the latter. Additionally, we demonstrate ties between the locality ordering problem and graph compression and show that prior methods from graph compression such as recursive graph bisection can be suitably adapted to this problem.