Computing the Face Lattice of a Polytope from its Vertex-Facet Incidences
Abstract
We give an algorithm that constructs the Hasse diagram of the face lattice of a convex polytope P from its vertex-facet incidences in time O(min{n,m}*a*f), where n is the number of vertices, m is the number of facets, a is the number of vertex-facet incidences, and f is the total number of faces of P. This improves results of Fukuda and Rosta (1994), who described an algorithm for enumerating all faces of a d-polytope in O(min{n,m}*d*f^2) steps. For simple or simplicial d-polytopes our algorithm can be specialized to run in time O(d*a*f). Furthermore, applications of the algorithm to other atomic lattices are discussed, e.g., to face lattices of oriented matroids.
Keywords
Cite
@article{arxiv.math/0106043,
title = {Computing the Face Lattice of a Polytope from its Vertex-Facet Incidences},
author = {Volker Kaibel and Marc E. Pfetsch},
journal= {arXiv preprint arXiv:math/0106043},
year = {2007}
}
Comments
14 pages; to appear in: Comput. Geom.; the new version contains some minor extensions and corrections as well as a more detailed treatment of oriented matroids