Solving Linear Programs in the Current Matrix Multiplication Time

Abstract

We show how to solve linear programs with accuracy epsilon in time n^{omega+o(1)} log(1/epsilon) where omega~2.3728639 is the current matrix multiplication constant. This hits a natural barrier of solving linear programs since linear systems is a special case of linear programs and solving linear systems require time n^{omega} currently.

Joint work with Michael B. Cohen and Zhao Song.