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A discussion of explicit methods for transitive closure computation based on matrix multiplication

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1 Author(s)
Macii, E. ; Dipartimento di Autom. e Inf., Politecnico di Torino, Italy

Arithmetic operations on matrices are applied to the problem of finding the transitive closure of a Boolean matrix. The best transitive closure algorithm known is based on the matrix multiplication method of Strassen (1959). It has been shown that this method requires, at most, O(n/sup /spl alpha///spl middot/P(n)) bit-wise operations, where /spl alpha/=log/sub 2/ 7, and P(n) bounds the number of bitwise operations needed for arithmetic module n+1. The problems of computing the transitive closure and computing the and-or product of Boolean matrices can then be considered of the same order of difficulty.

Published in:

Signals, Systems and Computers, 1995. 1995 Conference Record of the Twenty-Ninth Asilomar Conference on  (Volume:2 )

Date of Conference:

Oct. 30 1995-Nov. 1 1995