A Fast Search Algorithm for <m,m,m> Triple Product Property Triples and an Application for 5x5 Matrix Multiplication

Understand

We present a new fast search algorithm for <m,m,m> Triple Product Property (TPP) triples as defined by Cohn and Umans in 2003.

• The new algorithm achieves a speed-up factor of 40 up to 194 in comparison to the best known search algorithm.
• With a parallelized version of the new algorithm we are able to search for TPP triples in groups up to order 55.
• As an application we identify a list of groups that would realize 5x5 matrix multiplication with under 100 resp.