Fast sparse matrix multiplication

Raphael Yuster, Uri Zwick

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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(m0.7n1.2 + n2+o(1)) algebraic operations (i.e., multiplications, additions and subtractions) over R. For m ≤ n1.14, the new algorithm performs an almost optimal number of only n2+o(1) operations. For m ≤ n 1.68, the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses O(n2.38) 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. As the known fast rectangular matrix multiplication algorithms are far from being practical, our result, at least for now, is only of theoretical value.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsSusanne Albers, Tomasz Radzik
PublisherSpringer Verlag
Pages604-615
Number of pages12
ISBN (Print)3540230254, 9783540230250
DOIs
StatePublished - 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3221
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Bibliographical note

Funding Information:
Funded in part by the US National Science Foundation, Grant No. PHY89-22550.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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