Local Search for Fast Matrix Multiplication

  • Marijn J. H. HeuleEmail author
  • Manuel Kauers
  • Martina Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11628)


Laderman discovered a scheme for computing the product of two \(3\times 3\) matrices using only 23 multiplications in 1976. Since then, some more such schemes were proposed, but nobody knows how many such schemes there are and whether there exist schemes with fewer than 23 multiplications. In this paper we present two independent SAT-based methods for finding new schemes using 23 multiplications. Both methods allow computing a few hundred new schemes individually, and many thousands when combined. Local search SAT solvers outperform CDCL solvers consistently in this application.



The authors acknowledge the Texas Advanced Computing Center at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Marijn J. H. Heule
    • 1
    Email author
  • Manuel Kauers
    • 2
  • Martina Seidl
    • 3
  1. 1.Department of Computer ScienceThe University of TexasAustinUSA
  2. 2.Institute for AlgebraJ. Kepler UniversityLinzAustria
  3. 3.Institute for Formal Models and VerificationJ. Kepler UniversityLinzAustria

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