Work

Fast Matrix Multiplication

Year: 2015

Type: conference-paper

Abstract: Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time O(n2.3755). Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le~Gall has led to an improved algorithm running in time O(n2.3729). These algorithms are obtained by analyzing higher and higher tensor powers of a certain identity of Coppersmith and Winograd. We show that this exact approach cannot result in an algorithm with running time O(n2.3725), and identify a wide class of variants of this approach which cannot result in an algorithm with running time $O(n^{2.3078}); in particular, this approach cannot prove the conjecture that for every ε > 0, two n x n matrices can be multiplied in time O(n2+ε).

Source: ACM Symposium on Theory of Computing (STOC)

DOI: 10.1145/2746539.2746554

Authors: Andris Ambainis, Yuval Filmus, François Le Gall

Institutions: University of Latvia, Institute for Advanced Study, The University of Tokyo

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Japan Society for the Promotion of Science

Awards: New developments and applications of quantum algorithms for algebraic problems, Deepening Theory of Quantum Protocols, Research in Mathematics, Extended Formulations of Quantum Optimization and Their Applications to Classical/Quantum Computation