Naive multiplication of two N by N matrices requires N^3 scalar multiplications. For N=2, Strassen showed that it could be done in only R=7 < 8=N^3 multiplications. For N=3, it is known that 19 <= R <= 23, and for N=4 it is known that 34 <= R <= 49. This repository contains code that generates a mixed-integer linear program (MILP) formulation of the fast matrix multiplication problem for finding solutions with R < N^3 and proving that they are optimal. For a more detailed description, check out the accompanying manuscript.
To be able to generate MILP instances for various N and R, you need Python 3 along with the packages NumPy and PuLP. You can install these with conda env create if you have Anaconda or Miniconda, and then activate the environment with source activate fast-matrix-multiplication-env.
Once the environment is activated, simply run python model.py to generate a variety of MILP instances and initial solutions in the instances directory.
To solve an instance with Gurobi, run ./solve.sh fastxgemm-[parameters].lp from within the instances folder.