# Group-theoretic Algorithms for Matrix Multiplication

@inproceedings{Cohn2005GrouptheoreticAF,
title={Group-theoretic Algorithms for Matrix Multiplication},
author={Henry Cohn and Robert D. Kleinberg and Bal{\'a}zs Szegedy and Christopher Umans},
booktitle={FOCS},
year={2005}
}
• Published in FOCS 23 October 2005
• Computer Science, Mathematics
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication exponent less than 3, the asymptotically fastest of which achieves exponent 2.41. We present two conjectures regarding specific improvements, one combinatorial and the other algebraic. Either one…
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