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Fast Sparse Matrix Multiplication (2004)
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| Citations: | 53 - 3 self |
BibTeX
@MISC{Yuster04fastsparse,
author = {Raphael Yuster and Uri Zwick},
title = {Fast Sparse Matrix Multiplication},
year = {2004}
}
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Abstract
Let A and B two n n matrices over a ring R (e.g., the reals or the integers) each containing at most m non-zero elements. We present a new algorithm that multiplies A and B using O(m ) algebraic operations (i.e., multiplications, additions and subtractions) over R. The naive matrix multiplication algorithm, on the other hand, may need to perform #(mn) operations to accomplish the same task. For , the new algorithm performs an almost optimal number of only n operations. For m the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses O(n ) algebraic operations. The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast rectangular matrix multiplication algorithms. We also obtain improved algorithms for the multiplication of more than two sparse matrices.
Keyphrases
new algorithm fast sparse matrix multiplication algebraic operation known matrix multiplication algorithm simple combinatorial idea optimal number dense matrix non-zero element improved algorithm rectangular matrix multiplication algorithm naive matrix multiplication algorithm straightforward combination sparse matrix
