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Classic cache-oblivious parallel matrix multiplication algorithms achieveoptimality either in time or space, but not both, which promotes lots ofresearch on the best possible balance or tradeoff of such algorithms. We studymodern processor-oblivious runtime systems and figure out several ways toimprove algorithm's time bound while still bounding space and cacherequirements to be asymptotically optimal. By our study, we give out sublineartime, optimal work, space and cache algorithms for both general matrixmultiplication on a semiring and Strassen-like fast algorithm. Our experimentsalso show such algorithms have empirical advantages over classic counterparts.Our study provides new insights and research angles on how to optimizecache-oblivious parallel algorithms from both theoretical and empiricalperspectives.

Improving the Space-Time Efficiency of Processor-Oblivious Matrix Multiplication Algorithms