An optimal storage format for sparse matrices

Montagne, Eurípides; Ekambaram, Anand

doi:10.1016/j.ipl.2004.01.014

Cited by 38 publications

(17 citation statements)

References 1 publication

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“…Frontier Gather (per step) (lines [8][9] Each processor is given the segment of the frontier corresponding to their assigned submatrix.…”

Section: Parallel and Distributed Bfs Algorithmmentioning

confidence: 99%

“…There are other known sparse matrix formats that do not utilize row-starts [9], significantly saving memory; however, although such formats would be useful for algorithms that systematically iterate over all elements of a matrix, they perform badly for BFS where individual accesses to the edges of a given vertex need to be efficient.…”

Section: Other Sparse Matrix Formatsmentioning

confidence: 99%

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Efficient Breadth-First Search on Massively Parallel and Distributed-Memory Machines

et al. 2017

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“…Frontier Gather (per step) (lines [8][9] Each processor is given the segment of the frontier corresponding to their assigned submatrix.…”

Section: Parallel and Distributed Bfs Algorithmmentioning

confidence: 99%

Section: Other Sparse Matrix Formatsmentioning

confidence: 99%

Efficient Breadth-First Search on Massively Parallel and Distributed-Memory Machines

et al. 2017

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“…Transposed jagged diagonal format (TJAD) optimizes the amount of storage needed for a sparse matrix by eliminating the need for storing the permutation vector [4]. However, this forces a shift of indirect addressing from the multiplied vector to the result vector.…”

Section: Optimizing the Storagementioning

confidence: 99%

Performance Improvement of Sparse Matrix Vector Product on Vector Machines

Tiyyagura

Küster

Borowski³

2006

Computational Science – ICCS 2006

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Abstract. Many applications based on finite element and finite difference methods include the solution of large sparse linear systems using preconditioned iterative methods. Matrix vector multiplication is one of the key operations that has a significant impact on the performance of any iterative solver. In this paper, recent developments in sparse storage formats on vector machines are reviewed. Then, several improvements to memory access in the sparse matrix vector product are suggested. Particularly, algorithms based on dense blocks are discussed and reasons for their superior performance are explained. Finally, the performance gain by the presented modifications is demonstrated.

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“…Another array row_ind() is needed to store the row indices of the non-zero elements in the original matrix. Finally, a third array is also needed, tjd_ptr(), which stores the starting position of the transposed jagged diagonals in the array val() [17,18]. Although TJDS suffers the drawback of indirect addressing, it does not need the permutation step.…”

Section: Transposed Jagged Diagonal Storage (Tjds)mentioning

confidence: 99%

Review of Storage Techniques for Sparse Matrices

Shahnaz

Usman

Chughtai

2005

2005 Pakistan Section Multitopic Conference

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This paper reviews the current state of knowledge of the storage formats for sparse linear systems. Here we consider the ways developed so far for storing a sparse matrix and their quoted effects on computational speed. The main idea behind these formats involves keeping both the indices and the non-zero elements in the sparse matrix in a single data structure. These specialized schemes not only save storage but also yield computational savings. Since the locations of the non-zero elements in the matrix are known explicitly, unnecessary computations involving zeros can be avoided [1,2]. Thus the use of these formats reduces additional memory required in the usual indexing based storage schemes and gives promising performance improvements [3,4].

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An optimal storage format for sparse matrices

Cited by 38 publications

References 1 publication

Efficient Breadth-First Search on Massively Parallel and Distributed-Memory Machines

Efficient Breadth-First Search on Massively Parallel and Distributed-Memory Machines

Performance Improvement of Sparse Matrix Vector Product on Vector Machines

Review of Storage Techniques for Sparse Matrices

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