On minimum witnesses for boolean matrix multiplication

Keren Cohen, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


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)/ log2 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 (n1.939m0.318). In particular, if ω-1<α<2 where m=n α, the new algorithm is faster than both of the aforementioned algorithms.

Original languageEnglish
Pages (from-to)431-442
Number of pages12
Issue number2
StatePublished - Jun 2014


  • Boolean matrix multiplication
  • Minimum witness

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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