AI Chat AI Image Generator AI Video Text to Speech

Flip Graphs for Matrix Multiplication

12/02/2022

∙

by Manuel Kauers, et al.

∙

∙

We introduce a new method for discovering matrix multiplication schemes based on random walks in a certain graph, which we call the flip graph. Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5), both in characteristic two and for arbitrary ground fields.

Manuel Kauers
30 publications
Jakob Moosbauer
5 publications

research

∙ 05/13/2022

Skew-sparse matrix multiplication

Based on the observation that ℚ^(p-1) × (p-1) is isomorphic to a quotien...

0 Qiao-Long Huang, et al. ∙

research

∙ 09/22/2016

Scaling betweenness centrality using communication-efficient sparse matrix multiplication

Betweenness centrality (BC) is a crucial graph problem that measures the...

0 Edgar Solomonik, et al. ∙

research

∙ 06/01/2022

A Normal Form for Matrix Multiplication Schemes

Schemes for exact multiplication of small matrices have a large symmetry...

0 Manuel Kauers, et al. ∙

research

∙ 04/17/2023

Graph Sparsification by Approximate Matrix Multiplication

Graphs arising in statistical problems, signal processing, large network...

0 Neophytos Charalambides, et al. ∙

research

∙ 02/26/2020

A Systematic Survey of General Sparse Matrix-Matrix Multiplication

SpGEMM (General Sparse Matrix-Matrix Multiplication) has attracted much ...

0 Jianhua Gao, et al. ∙

research

∙ 04/11/2019

The MOMMS Family of Matrix Multiplication Algorithms

As the ratio between the rate of computation and rate with which data ca...

0 Tyler M. Smith, et al. ∙

research

∙ 03/03/2020

Graphs and codes produced by a new method for dividing a natural number by two

In this paper, we introduce a new method which we call it MZ-method, for...

0 M. Zeynali Azim, et al. ∙