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Local Search for Fast Matrix Multiplication

Part of the Lecture Notes in Computer Science book series (LNTCS,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.

M. J. H. Heule is supported by NSF grant CCF-1813993 and AFRL Award FA8750-15-2-0096.

M. Kauers is supported by the Austrian FWF grants P31571-N32 and F5004.

M. Seidl is supported by the Austrian FWF grant NFN S11408-N23 and the LIT AI Lab funded by the State of Upper Austria.

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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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Correspondence to Marijn J. H. Heule .

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Heule, M.J.H., Kauers, M., Seidl, M. (2019). Local Search for Fast Matrix Multiplication. In: Janota, M., Lynce, I. (eds) Theory and Applications of Satisfiability Testing – SAT 2019. SAT 2019. Lecture Notes in Computer Science(), vol 11628. Springer, Cham.

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