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TREEBASED SPACE EFFICIENT FORMATS FOR STORING THE STRUCTURE OF SPARSE MATRICES ∗
"... Sparse storage formats describe a way how sparse matrices are stored in a computer memory. Extensive research has been conducted about these formats in the context of performance optimization of the sparse matrixvector multiplication algorithms, but memory efficient formats for storing sparse matri ..."
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Sparse storage formats describe a way how sparse matrices are stored in a computer memory. Extensive research has been conducted about these formats in the context of performance optimization of the sparse matrixvector multiplication algorithms, but memory efficient formats for storing sparse matrices are still under development, since the commonly used storage formats (like COO or CSR) are not sufficient. In this paper, we propose and evaluate new storage formats for sparse matrices that minimize the space complexity of information about matrix structure. The first one is based on arithmetic coding and the second one is based on binary tree format. We compare the space complexity of common storage formats and our new formats and prove that the latter are considerably more space efficient. Key words: sparse matrix representation; parallel execution; space efficiency; arithmeticalcodingbased format; minimal binary tree format; minimal quadtree format; AMS subject classifications. 68M14, 68W10, 68P05, 68P20, 94A17
Implementation for Shared Memory Parallel Computers
"... Prof. Daniel P. Bovet“Ladies and gentleman, this is your captain speaking. I have some good news and I have some bad news. The good news is, that we have a very strong tail wind, and we are doing one thousand four hundred miles per hour over land. The bad news is, that all of our navigation instrume ..."
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Prof. Daniel P. Bovet“Ladies and gentleman, this is your captain speaking. I have some good news and I have some bad news. The good news is, that we have a very strong tail wind, and we are doing one thousand four hundred miles per hour over land. The bad news is, that all of our navigation instruments are out, and we don’t know where we are, and we don’t know where we are going.”
Proceedings of the Federated Conference on Computer Science and Information Systems pp. 439–442 ISBN 9788360810224 Developing an OO Model for Generalized Matrix Multiplication: Preliminary Considerations
"... Abstract—Recent changes in computational sciences force reevaluation of the role of dense matrix multiplication. Among others, this resulted in a proposal to consider generalized matrix multiplication, based on the theory of algebraic semirings. The aim of this note is to outline an initial object o ..."
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Abstract—Recent changes in computational sciences force reevaluation of the role of dense matrix multiplication. Among others, this resulted in a proposal to consider generalized matrix multiplication, based on the theory of algebraic semirings. The aim of this note is to outline an initial object oriented model of the generalized matrixmultiplyadd operation. I.
GENERALIZED MATRIX MULTIPLICATION AND ITS OBJECT ORIENTED MODEL
"... Since the beginning of the 21st century, we observe rapid changes in the area of, broadly understood, computational sciences. One of interesting eects of these changes is the need for reevaluation of the role of dense matrix multiplication. The aim of this paper is twofold. First, to summarize deve ..."
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Since the beginning of the 21st century, we observe rapid changes in the area of, broadly understood, computational sciences. One of interesting eects of these changes is the need for reevaluation of the role of dense matrix multiplication. The aim of this paper is twofold. First, to summarize developments that point toward a need for reconsidering usefulness of matrix multiplication generalized on the basis of the theory of algebraic semirings. Second, to propose generalized matrixmatrix multiplyandupdate (MMU) operation and its object oriented model. Key words: matrix multiplication, algebraic semirings, algebraic path problem AMS subject classications. 65F30, 13A99 1. Introduction. Recently