A Conversion Procedure for NNC Polyhedra

TL;DR

This paper introduces a new conversion procedure for NNC polyhedra that improves efficiency by avoiding slack variables, addressing technical issues in existing methods, and demonstrating significant performance gains.

Contribution

It presents a novel Double Description representation and Chernikova-like conversion algorithm for NNC polyhedra that enhances efficiency and simplifies encoding.

Findings

Achieves significant efficiency improvements over existing implementations

Eliminates the need for slack variables in the representation

Addresses technical issues in encoding NNC polyhedra

Abstract

We present an alternative Double Description representation for the domain of NNC (not necessarily topologically closed) polyhedra, together with the corresponding Chernikova-like conversion procedure. The representation differs from the ones adopted in the currently available implementations of the Double Description method in that it uses no slack variable at all: this new approach provides a solution to a few technical issues caused by the encoding of an NNC polyhedron as a closed polyhedron in a higher dimension space. A preliminary experimental evaluation shows that the new conversion algorithm is able to achieve significant efficiency improvements with respect to state-of-the-art implementations.