Computing the Face Lattice of a Polytope from its Vertex-Facet Incidences

dc.creatorKaibel, Volker
dc.creatorPfetsch, Marc E.
dc.date2001-06-07
dc.date2002-08-14
dc.date.accessioned2026-07-07T04:42:01Z
dc.date.available2026-07-07T04:42:01Z
dc.descriptionWe 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.
dc.description14 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
dc.identifierhttps://arxiv.org/abs/math/0106043
dc.identifierhttp://arxiv.org/abs/math/0106043
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61601
dc.subjectMetric Geometry
dc.subjectCombinatorics
dc.subject68R05 68U05 52B11 68Q25 52C40
dc.titleComputing the Face Lattice of a Polytope from its Vertex-Facet Incidences
dc.typetext

Files

Collections