Witnesses for Boolean Matrix Multiplication and for Transitive Closure

Zvi Galil; Olded Margalit

doi:10.1006/jcom.1993.1014

Witnesses for Boolean Matrix Multiplication and for Transitive Closure

Zvi Galil, Olded Margalit

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

The subcubic (O(n^ω) for ω < 3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C = A · B but if C_ij = 1 they do not find an index k (a witness) such that A_ik = B_kj = 1. We design a deterministic algorithm for computing the matrix of witnesses which runs in O(n^{ω + ε}) time for any positive e. We also design an algorithm that computes witnesses for the transitive closure in the same time needed to compute witnesses for Boolean matrix multiplication.

Original language	English
Pages (from-to)	201-221
Number of pages	21
Journal	Journal of Complexity
Volume	9
Issue number	2
DOIs	https://doi.org/10.1006/jcom.1993.1014
State	Published - 1 Jan 1993
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Statistics and Probability
Numerical Analysis
General Mathematics
Control and Optimization
Applied Mathematics

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10.1006/jcom.1993.1014

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Witnesses for Boolean Matrix Multiplication and for Transitive Closure

Abstract

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