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Sparse matrix-matrix multiplication (SpGEMM) is an important primitive for many data analytics algorithms, such as Markov clustering. Unlike the dense case, where performance of matrix-matrix multiplication is considerably higher than matrix-vector multiplication, the opposite is true for the sparse case on GPUs. A signi cant challenge is that the sparsity structure of the output sparse matrix is not known a priori, and many additive contributions must be combined to generate its non-zero elements. We use synthetic matrices to characterize the e ectiveness of alternate approaches and devise a hybrid approach that is demonstrated to be consistently superior to other available GPU SpGEMM implementations.

Widespread use of stochastic flow based graph clustering algorithms, e.g. Markov Clustering (MCL), has been hampered by their lack of scalability and fragmentation of output. Multi-Level Regularized Markov Clustering (MLR-MCL) is an improvement over Markov Clustering (MCL), providing faster performance and better quality of clusters for large graphs. However, a closer look at MLR-MCL's performance reveals potential for further improvement. In this paper we present a fast parallel implementation of MLR-MCL algorithm via static work partitioning based on analysis of memory footprints. By parallelizing the most time consuming region of the sequential MLR-MCL algorithm, we report up to 10.43x (5.22x in average) speedup on CPU, using 8 datasets from SNAP and 3 PPI datasets. In addition, our algorithm can be adapted to perform general sparse matrix-matrix multiplication (SpGEMM), and our experimental evaluation shows up to 3.50x (1.92x in average) speedup on CPU, and up to 5.12x (2.20x in average) speedup on MIC, comparing to the SpGEMM kernel provided by Intel Math Kernel Library (MKL).

SUMMARYQuantum Monte Carlo (QMC) applications perform simulation with respect to an initial state of the quantum mechanical system, which is often captured by using a cubic B-spline basis. This representation is stored as a read-only table of coefficients and accesses to the table are generated at random as part of the Monte Carlo simulation. Current QMC applications, such as QWalk and QMCPACK, replicate this table at every process or node, which limits scalability because increasing the number of processors does not enable larger systems to be run. We present a partitioned global address space approach to transparently managing this data using Global Arrays in a manner that allows the memory of multiple nodes to be aggregated. We develop an automated data management system that significantly reduces communication overheads, enabling new capabilities for QMC codes. Experimental results with QWalk and QMCPACK demonstrate the effectiveness of the data management system.

Quantum Monte Carlo (QMC) applications perform simulation with respect to an initial state of the quantum mechanical system, which is often captured by using a cubic B-spline basis. This representation is stored as a read-only table of coefficients, and accesses to the table are generated at random as part of the Monte Carlo simulation. Current QMC applications such as QWalk and QMCPACK, replicate this table at every process or node, which limits scalability because increasing the number of processors does not enable larger systems to be run. We present a partitioned global address space (PGAS) approach to transparently managing this data using Global Arrays in a manner that allows the memory of multiple nodes to be aggregated. We develop an automated data management system that significantly reduces communication overheads, enabling new capabilities for QMC codes. Experimental results with the QWalk application demonstrate the effectiveness of the data management system.

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