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Contents
What is Polyhedral Computation FAQ?
Convex Polyhedron
What is convex polytope/polyhedron?
What are the faces of a convex polytope/polyhedron?
What is the face lattice of a convex polytope
What is a dual of a convex polytope?
What is simplex?
What is cube/hypercube/cross polytope?
What is simple/simplicial polytope?
What is 0-1 polytope?
What is the best upper bound of the numbers of -dimensional faces of a -polytope with vertices?
What is convex hull? What is the convex hull problem?
What is the Minkowski-Weyl theorem for convex polyhedra?
What is the vertex enumeration problem, and what is the facet enumeration problem?
How can one enumerate all faces of a convex polyhedron?
What computer models are appropriate for the polyhedral computation?
How do we measure the complexity of a convex hull algorithm?
How many facets does the average polytope with vertices in have?
How many facets can a 0-1 polytope with vertices in have?
How hard is it to verify that an H-polyhedron and a V-polyhedron are equal?
Is there an efficient way of determining whether a given point is in the convex hull of a given finite set of points in ?
How can one remove all interior points of from for large clouds of points in ?
Is there any efficient algorithm to remove redundant inequalities from a system of linear inequalities
Is there any efficient algorithm to compute the intersection of two (or ) polytopes
Is there any efficient algorithm to compute the volume of a convex polytope in ?
Voronoi Diagram and Delaunay Triangulation
What is cell complex? What is triangulation?
What is Voronoi diagram in ?
What is the Delaunay triangulation in ?
Computing the Delaunay complex and the Voronoi diagram. What does it mean and how to do it with available software?
Is it possible to compute only the adjacencies of Voronoi cells in the Voronoi diagram efficiently?
Is it possible to compute only the edges of the Delaunay complex (triangulation) ?
Is it possible to determine the Delaunay cell containing a given point efficiently?
What is the best upper bound of the numbers of simplices in the Delaunay triangulation?
Linear Programming
What is LP?
Polyhedral Computation Codes
Acknowledgements
Bibliography
About this document ...
Komei Fukuda 2004-08-26