Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm

TL;DR

This paper introduces new memory-efficient schedules for Strassen-Winograd's matrix multiplication, reducing memory needs through pre-additions, overwriting inputs, or recursive classical multiplication, including two fully in-place methods.

Contribution

The paper presents novel in-place and memory-efficient scheduling strategies for Strassen-Winograd's algorithm, developed via an exhaustive search approach.

Findings

Two fully in-place schedules demonstrated

Memory requirements reduced by three means

Implementation used pebble game-based search

Abstract

We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices, or by using a first recursive level of classical multiplication. In particular, we show two fully in-place schedules: one having the same number of operations, if the input matrices can be overwritten; the other one, slightly increasing the constant of the leading term of the complexity, if the input matrices are read-only. Many of these schedules have been found by an implementation of an exhaustive search algorithm based on a pebble game.