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On the Representation and Multiplication of Hypersparse Matrices
, 2008
"... Multicore processors are marking the beginning of a new era of computing where massive parallelism is available and necessary. Slightly slower but easy to parallelize kernels are becoming more valuable than sequentially faster kernels that are unscalable when parallelized. In this paper, we focus on ..."
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Cited by 9 (7 self)
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Multicore processors are marking the beginning of a new era of computing where massive parallelism is available and necessary. Slightly slower but easy to parallelize kernels are becoming more valuable than sequentially faster kernels that are unscalable when parallelized. In this paper, we focus on the multiplication of sparse matrices (SpGEMM). We first present the issues with existing sparse matrix representations and multiplication algorithms that make them unscalable to thousands of processors. Then, we develop and analyze two new algorithms that overcome these limitations. We consider our algorithms first as the sequential kernel of a scalable parallel sparse matrix multiplication algorithm and second as part of a polyalgorithm for SpGEMM that would execute different kernels depending on the sparsity of the input matrices. Such a sequential kernel requires a new data structure that exploits the hypersparsity of the individual submatrices owned by a single processor after the 2D partitioning. We experimentally evaluate the performance and characteristics of our algorithms and show that they scale significantly better than existing kernels.
On the Enhancements of a Sparse Matrix Information Retrieval Approach
 Proceedings of the International Conference on Parallel and distributed Processing Techniques and Applications
, 2000
"... A novel approach to information retrieval is proposed and evaluated. By representing an inverted index as a sparse matrix, matrixvector multiplication algorithms can be used to query the index. As many parallel sparse matrix multiplication algorithms exist, such an information retrieval approach le ..."
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Cited by 8 (2 self)
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A novel approach to information retrieval is proposed and evaluated. By representing an inverted index as a sparse matrix, matrixvector multiplication algorithms can be used to query the index. As many parallel sparse matrix multiplication algorithms exist, such an information retrieval approach lends itself to parallelism. This enables us to attack the problem of parallel information retrieval, which has resisted good scalability. We evaluate our proposed approach using several document collections from within the commonly used NIST TREC corpus. Our results indicate that our approach saves approximately 30% of the total storage requirements for the inverted index. Additionally, to improve accuracy, we develop a novel matrix based, relevance feedback technique as well as a proximity search algorithm. 1 Introduction With constantly growing text resources, efficiency improvements via parallel processing, storage space reduction and the improvement of search effectiveness are the main ...
Highly Parallel Sparse MatrixMatrix Multiplication
, 2010
"... Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on ..."
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Cited by 6 (3 self)
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Generalized sparse matrixmatrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an unbounded number of processors. Our algorithms are based on twodimensional block distribution of sparse matrices where serial sections use a novel hypersparse kernel for scalability. We give a stateoftheart MPI implementation of one of our algorithms. Our experiments show scaling up to thousands of processors on a variety of test scenarios.
CachingEfficient Multithreaded Fast Multiplication Of Sparse Matrices
 Proceedings 12the International Parallel Processing Symposium
, 1998
"... Several fast sequential algorithms have been proposed in the past to multiply sparse matrices. These algorithms do not explicitly address the impact of caching on performance. We show that a rather simple sequential cacheefficient algorithm provides significantly better performance than existing a ..."
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Cited by 4 (0 self)
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Several fast sequential algorithms have been proposed in the past to multiply sparse matrices. These algorithms do not explicitly address the impact of caching on performance. We show that a rather simple sequential cacheefficient algorithm provides significantly better performance than existing algorithms for sparse matrix multiplication. We then describe a multithreaded implementation of this simple algorithm and show that its performance scales well with the number of threads and CPUs. For 10% sparse, 500 X 500 matrices, the multithreaded version running on 4CPU systems provides more than a 41.1fold speed increase over the wellknown BLAS routine and a 14.6 fold and 44.6fold speed increase over two other recent techniques for fast sparse matrix multiplication, both of which are relatively difficult to parallelize efficiently. Keywords: sparse matrix multiplication, caching, loop interchanging 1. Introduction The need to efficiently multiply two sparse matrices is critica...