Automatic reproduction of a genius algorithm: Strassen's algorithm revisited by genetic search

Authors:
Seunghyun Oh;Byung-Ro Moon
Affiliations:
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI;Optimization and Investment Engineering Laboratory, School of Computer Science and Engineering, Seoul National University, Seoul, Korea
Venue:
IEEE Transactions on Evolutionary Computation
Year:
2010

Citing 8
Cited 1

How to multiply matrices faster

How to multiply matrices faster
Matrix multiplication via arithmetic progressions

Journal of Symbolic Computation - Special issue on computational algebraic complexity
Genetic Algorithms in Search, Optimization and Machine Learning

Genetic Algorithms in Search, Optimization and Machine Learning
Introduction to Algorithms

Introduction to Algorithms
Genetic Algorithm and Graph Partitioning

IEEE Transactions on Computers
Efficient Procedures for Using Matrix Algorithms

Proceedings of the 2nd Colloquium on Automata, Languages and Programming
A Nonlinear Mapping for Data Structure Analysis

IEEE Transactions on Computers
Some techniques for proving certain simple programs optimal

SWAT '69 Proceedings of the 10th Annual Symposium on Switching and Automata Theory (swat 1969)

A parallel implementation of Strassen's matrix multiplication algorithm for wormhole-routed all-port 2D torus networks

The Journal of Supercomputing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In 1968, Volker Strassen, a young German mathematician, announced a clever algorithm to reduce the asymptotic complexity of n × n matrix multiplication from the order of n3 to n2.81. It soon became one of the most famous scientific discoveries in the 20th century and provoked numerous studies by other mathematicians to improve upon it. Although a number of improvements have been made, Strassen's algorithm is still optimal in his original framework, the bilinear systems of 2 × 2 matrix multiplication, and people are still curious how Strassen developed his algorithm. We examined it to see if we could automatically reproduce Strassen's discovery using a search algorithm and find other algorithms of the same quality. In total, we found 608 algorithms that have the same quality as Strassen's, including Strassen's original algorithm. We partitioned the algorithms into nine different groups based on the way they are constructed. This paper was made possible by the combination of genetic search and linear-algebraic techniques. To the best of our knowledge, this is the first work that automatically reproduced Strassen's algorithm, and furthermore, discovered new algorithms with equivalent asymptotic complexity using a search algorithm.