The convex hull of a regular set of integer vectors is polyhedral and effectively computable

TL;DR

This paper proves that the convex hull of a regular set of integer vectors, represented by Number Decision Diagrams, is a polyhedron that can be effectively computed, advancing symbolic geometric analysis.

Contribution

It establishes that the convex hull of sets represented by NDDs is polyhedral and provides a method for its effective computation.

Findings

Convex hull of NDD-represented sets is polyhedral.

Convex hull can be effectively computed from NDDs.

Advances symbolic geometric analysis of integer vector sets.

Abstract

Number Decision Diagrams (NDD) provide a natural finite symbolic representation for regular set of integer vectors encoded as strings of digit vectors (least or most significant digit first). The convex hull of the set of vectors represented by a NDD is proved to be an effectively computable convex polyhedron.