Enumerating integer points in polytopes with bounded subdeterminants

TL;DR

This paper presents a polynomial-time algorithm for enumerating the vertices of the convex hull of integer points in polytopes with constraint matrices having bounded and nonzero subdeterminants, extending previous optimization results.

Contribution

It introduces a method to enumerate vertices of such polytopes efficiently, broadening the scope of polynomial-time algorithms in integer programming.

Findings

Enumeration of vertices is polynomial in dimension and size.

Extends previous polynomial-time optimization results.

Applicable to polytopes with bounded subdeterminants.

Abstract

We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This extends a previous result by Artmann et al. who showed that integer linear optimization in such polytopes can be done in polynomial time.