, Volume 16, Issue 4–5, pp 434–449 | Cite as

Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions

  • N. Alon
  • M. Naor


Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, solves the problem of computingwitnesses for the Boolean product of two matrices. That is, ifA andB are twon byn matrices, andC=AB is their Boolean product, the algorithm finds for every entryC ij =1 a witness: an indexk so thatA ik =B kj =1. Its running time exceeds that of computing the product of twon byn matrices with small integer entries by a polylogarithmic factor. The second algorithm is a nearly linear time deterministic procedure for constructing a perfect hash function for a givenn-subset of {1,...,m}.

Key words

Derandomization Matrix multiplication Perfect hashing 


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Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • N. Alon
    • 1
  • M. Naor
    • 2
  1. 1.Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Department of Applied Mathematics and Computer ScienceWeizmann InstituteRehovotIsrael

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