Approximating optimal transport with linear programs

TL;DR

This paper presents a method to approximate optimal transport efficiently by reducing the problem to relative approximations of positive linear programs, leading to faster algorithms in certain cost regimes.

Contribution

It introduces a novel reduction from optimal transport approximation to positive linear program approximation, enabling improved computational efficiency.

Findings

Faster additive approximation algorithms for optimal transport.

Reduction of optimal transport approximation to positive linear programs.

Applicable in regimes with bounded transportation costs.

Abstract

In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation algorithms for optimal transport.