Extended Formulations for Polytopes of Regular Matroids

TL;DR

This paper proves that the base and independence polytopes of rank n regular matroids over m elements have an extension complexity that scales linearly with m and n, simplifying understanding of their geometric complexity.

Contribution

The paper provides a straightforward proof establishing that regular matroid polytopes have extension complexity O(mn), clarifying their geometric properties.

Findings

Base and independence polytopes of regular matroids have extension complexity O(mn)

The proof simplifies previous understanding of matroid polytope complexity

Extension complexity scales linearly with matroid size and rank

Abstract

We present a simple proof of the fact that the base (and independence) polytope of a rank $n$ regular matroid over $m$ elements has an extension complexity $O(mn)$.