A fast output-sensitive algorithm for Boolean matrix multiplication

Summary, in English

We use randomness to exploit the potential sparsity of the Boolean matrix product in order to speed up the computation of the product. Our new fast output-sensitive algorithm for Boolean matrix product and its witnesses is randomized and provides the Boolean product and its witnesses almost certainly. Its worst-case time performance is expressed in terms of the input size and the number of non-zero entries of the product matrix. It runs in time (O) over tilde (n(2)s(w/2-1)), where the input matrices have size n, X 11,, the number of non-zero entries in the product matrix is at most.s, w is the exponent of the fast matrix multiplication and 0( f (n,)) denotes 0(f) logd 71) for some constant d. By the currently best bound on w, its running time can be also expressed as 0(712s0"188). Our algorithm is substantially faster than the output-sensitive column-row method for Boolean matrix product for s larger than n1.232 and it is never slower than the fast 0(r')time algorithm for this problem. We also present a partial derandomization of our algorithm as well as its generalization to include the Boolean product of rectangular Boolean matrices. Finally, we show several applications of our output-sensitive algorithms.

• Author: Andrzej Lingas
• Department/s: Computer Science
• Publishing year: 2009
• Language: English
• Pages: 408-419
• Publication/Series: Algorithms - ESA 2009, Proceedings
• Volume: 5757
• Links: http://dx.doi.org/10.1007/978-3-642-04128-0_37
• Document type: Conference paper
• Publisher: Springer
• Topic: Computer Science
• Conference name: 17th Annual European Symposium on Algorithms
• Conference date: 2009-09-07 - 2009-09-09
• Status: Published
• Project: VR 2008-4649
• ISBN/ISSN/Other: ISSN: 0302-9743; ISSN: 1611-3349