Faster multi-witnesses for Boolean matrix multiplication

Leszek Gasieniec, Mirosław Kowaluk, Andrzej Lingas

Research output: Contribution to journalArticle

11 Scopus citations

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 languageEnglish (US)
Pages (from-to)242-247
Number of pages6
JournalInformation Processing Letters
Volume109
Issue number4
DOIs
StatePublished - Jan 31 2009
Externally publishedYes

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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