Direct methods for sparse matrices
Direct methods for sparse matrices
Sparse matrix computations on parallel processor arrays
SIAM Journal on Scientific Computing
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Data distributions for sparse matrix vector multiplication
Parallel Computing
Automatic Data Structure Selection and Transformation for Sparse Matrix Computations
IEEE Transactions on Parallel and Distributed Systems
Parallel implementation of the Lanczos method for sparse matrices: analysis of data distributions
ICS '96 Proceedings of the 10th international conference on Supercomputing
Parallelization techniques for sparse matrix applications
Journal of Parallel and Distributed Computing - Special issue on compilation techniques for distributed memory systems
Matrix computations (3rd ed.)
Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
Vienna-Fortran/HPF Extensions for Sparse and Irregular Problems and Their Compilation
IEEE Transactions on Parallel and Distributed Systems
Parallel Computing - special issue on parallel computing for irregular applications
Automatic parallelization of irregular applications
Parallel Computing - special issue on parallel computing for irregular applications
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Parallel Sparse Supports for Array Intrinsic Functions of Fortran 90
The Journal of Supercomputing
Runtime Support and Compilation Methods for User-Specified Irregular Data Distributions
IEEE Transactions on Parallel and Distributed Systems
Partitioning an Array onto a Mesh of Processors
PARA '96 Proceedings of the Third International Workshop on Applied Parallel Computing, Industrial Computation and Optimization
A Parallel Algorithm for Computing the Extremal Eigenvalues of Very Large Sparse Matrices
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
On the Complexity of the Generalized Block Distribution
IRREGULAR '96 Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems
Parallel branch-and-cut for set partitioning
Parallel branch-and-cut for set partitioning
Fast sparse matrix-vector multiplication for TeraFlop/s computers
VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
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This paper introduces new approaches to the data distribution-partition problem for sparse matrices in a multiprocessor environment. In this work, the data partition problem of a sparse matrix is modeled as a Min-Max Problem subject to the uniformity constrain when the goal is to balance the load for both sparse and dense operations. This problem is NP-Complete and two heuristic solutions (ABO and GPB) are proposed. The key of ABO and GPB is to determine the permutation of rows/columns of the input sparse matrix to obtain a sorted matrix with a homogeneous density of nonzero elements. Due to the heuristic nature of the proposed methods their validation is carried out by a comparative study of the parallel efficiency of two types of problems (sparse and mixed) when ABO, GPB, Block, Cyclic and MRD data distributions are applied.