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

TL;DR

This paper introduces new processor-oblivious matrix multiplication algorithms that optimize time, space, and cache efficiency simultaneously, supported by theoretical analysis and empirical validation.

Contribution

It presents novel algorithms achieving sublinear time with optimal work, space, and cache bounds for general and Strassen-like matrix multiplication, improving upon classic methods.

Findings

Algorithms achieve sublinear time complexity.

Empirical results show advantages over traditional algorithms.

Provides new theoretical insights into cache-oblivious optimization.

Abstract

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.