### Abstract

A generalization of the the k-witness problem of computing a single witness in a Boolean matrix multiplication, where k witnesses are determined for each positive entry of the Boolean product, is studied. It is also shown that k-witness problem can be deterministically solved in certain a time by an algorithm based on rectangular matrix multiplication. The bounded k-witness problem is a variant of the bounded k-reconstruction problem, in which all witnesses are recovered for entries that have at most k witnesses. The results also shows that The k-witness problem for the Boolean product of two n dimensional matrices can be deterministically solved in a certain time, by the algorithm using rectangular matrix multiplication. It is also found that the randomized algorithm for the k-witness problem matches the lower bound at the two extremes of the matrix.

Original language | English (US) |
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Pages (from-to) | 242-247 |

Number of pages | 6 |

Journal | Information Processing Letters |

Volume | 109 |

Issue number | 4 |

DOIs | |

State | Published - Jan 31 2009 |

Externally published | Yes |

### Keywords

- Algorithms
- Analysis of algorithms
- Boolean matrix multiplication
- Combinatorial problems
- Lowest common ancestors in dags
- Time complexity, directed acyclic graph (dag)
- Witnesses for Boolean matrix product

### ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications

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## Cite this

*Information Processing Letters*,

*109*(4), 242-247. https://doi.org/10.1016/j.ipl.2008.10.012