Witnesses for Boolean Matrix Multiplication and for Transitive Closure

Zvi Galil, Olded Margalit

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The subcubic (O(nω) for ω < 3) algorithms to multiply Boolean matrices do not provide the witnesses; namely, they compute C = A · B but if Cij = 1 they do not find an index k (a witness) such that Aik = Bkj = 1. We design a deterministic algorithm for computing the matrix of witnesses which runs in O(nω + 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 languageEnglish
Pages (from-to)201-221
Number of pages21
JournalJournal of Complexity
Issue number2
StatePublished - 1 Jan 1993
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics (all)
  • Control and Optimization
  • Applied Mathematics


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