  Classic cache-oblivious parallel matrix multiplication algorithms achieve
optimality either in time or space, but not both, which promotes lots of
research on the best possible balance or tradeoff of such algorithms. We study
modern processor-oblivious runtime systems and figure out several ways to
improve algorithm's time bound while still bounding space and cache
requirements to be asymptotically optimal. By our study, we give out sublinear
time, optimal work, space and cache algorithms for both general matrix
multiplication on a semiring and Strassen-like fast algorithm. Our experiments
also show such algorithms have empirical advantages over classic counterparts.
Our study provides new insights and research angles on how to optimize
cache-oblivious parallel algorithms from both theoretical and empirical
perspectives.
