## Abstract

Minimum witnesses for Boolean matrix multiplication play an important role in several graph algorithms. For two Boolean matrices A and B of order n, with one of the matrices having at most m nonzero entries, the fastest known algorithms for computing the minimum witnesses of their product run in either O(n ^{2.575}) time or in O(n ^{2}+mnlog(n ^{2}/m)/ log^{2} n) time. We present a new algorithm for this problem. Our algorithm runs either in time Õ(n 3/4-ω m 1-1/4-ω) where ω<2.376 is the matrix multiplication exponent, or, if fast rectangular matrix multiplication is used, in time O (n^{1.939}m^{0.318}). In particular, if ω-1<α<2 where m=n ^{α}, the new algorithm is faster than both of the aforementioned algorithms.

Original language | English |
---|---|

Pages (from-to) | 431-442 |

Number of pages | 12 |

Journal | Algorithmica |

Volume | 69 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2014 |

Externally published | Yes |

## Keywords

- Boolean matrix multiplication
- Minimum witness