Fast Boolean matrix multiplication for highly clustered data
Author
Summary, in English
We consider the problem of computing the product of two
n×n Boolean matrices A and B. For an n×n Boolean matrix C, let GC
be the complete weighted graph on the rows of C where the weight of an
edge between two rows is equal to its Hamming distance, i.e., the number
of entries in the first row having values different from the corresponding
entries in the second one. Next, letMWT(C) be the weight of a minimum
weight spanning tree of GC. We show that the product of A with B as
well as the so called witnesses of the product can be computed in time
(n(n + min{MWT(A),MWT(Bt)}))
˜O
n×n Boolean matrices A and B. For an n×n Boolean matrix C, let GC
be the complete weighted graph on the rows of C where the weight of an
edge between two rows is equal to its Hamming distance, i.e., the number
of entries in the first row having values different from the corresponding
entries in the second one. Next, letMWT(C) be the weight of a minimum
weight spanning tree of GC. We show that the product of A with B as
well as the so called witnesses of the product can be computed in time
(n(n + min{MWT(A),MWT(Bt)}))
˜O
Department/s
- Department of Computer Science
- Computer Science
- Parallel Systems
Publishing year
2001
Language
English
Pages
258-263
Publication/Series
Algorithms and data structures : 7th International Workshop, WADS 2001, Providence, RI, USA, August 8-10, 2001 : proceedings
Volume
LNCS 2125
Full text
- Available as PDF - 107 kB
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Document type
Conference paper
Publisher
Springer
Topic
- Computer Science
Status
Published
ISBN/ISSN/Other
- ISBN: 3540424237