Computing the bounded subcomplex of an unbounded polyhedron

TL;DR

This paper develops efficient algorithms to compute the Hasse diagram of bounded faces in unbounded polyhedra, with special focus on simple polyhedra, supported by computational experiments.

Contribution

It introduces new combinatorial algorithms for bounded face enumeration in unbounded polyhedra, including a specialized approach for simple polyhedra.

Findings

Algorithms successfully produce Hasse diagrams for bounded faces.

Computational results demonstrate efficiency and practicality.

Special case of simple polyhedra is effectively handled.

Abstract

We study efficient combinatorial algorithms to produce the Hasse diagram of the poset of bounded faces of an unbounded polyhedron, given vertex-facet incidences. We also discuss the special case of simple polyhedra and present computational results.