1 research outputs found
Sparsifying the Operators of Fast Matrix Multiplication Algorithms
Fast matrix multiplication algorithms may be useful, provided that their
running time is good in practice. Particularly, the leading coefficient of
their arithmetic complexity needs to be small. Many sub-cubic algorithms have
large leading coefficients, rendering them impractical. Karstadt and Schwartz
(SPAA'17, JACM'20) demonstrated how to reduce these coefficients by sparsifying
an algorithm's bilinear operator. Unfortunately, the problem of finding optimal
sparsifications is NP-Hard.
We obtain three new methods to this end, and apply them to existing fast
matrix multiplication algorithms, thus improving their leading coefficients.
These methods have an exponential worst case running time, but run fast in
practice and improve the performance of many fast matrix multiplication
algorithms. Two of the methods are guaranteed to produce leading coefficients
that, under some assumptions, are optimal