IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2021-10-18T13:48:33ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2011-07-27T09:32:44Z2014-07-17T12:39:20Zhttp://eprints.imtlucca.it/id/eprint/468This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4682011-07-27T09:32:44ZConvexity recognition of the union of polyhedraIn this paper we consider the following basic problem in polyhedral computation: Given two polyhedra in Rd, P and Q, decide whether their union is convex, and, if so, compute it. We consider the three natural specializations of the problem: 1) when the polyhedra are given by halfspaces (H-polyhedra), 2) when they are given by vertices and extreme rays (V-polyhedra), and 3) when both H- and V-polyhedral representations are available. Both the bounded (polytopes) and the unbounded case are considered. We show that the first two problems are polynomially solvable, and that the third problem is strongly-polynomially solvable.Alberto Bemporadalberto.bemporad@imtlucca.itKomei FukudaFabio Danilo Torrisi2011-07-27T09:11:28Z2014-07-17T12:18:14Zhttp://eprints.imtlucca.it/id/eprint/571This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5712011-07-27T09:11:28ZOn convexity recognition of the union of polyhedra
In this paper we consider the following basic problem in polyhedral computation: given two polyhedra in $R^d$, $P$ and $Q$, decide whether their union is convex, and eventually compute it. We consider the three natural specializations of the problem: 1) when the polyhedra are given by half-spaces (H-polyhedra) 2) when they are given by vertices and extreme rays (V-polyhedra) 3) when both H- and V-polyhedral representations are available. Both the bounded (polytopes) and the unbounded case are considered. We show that the first two problems are polynomially solvable, and that the third problem is solvable in linear time.Alberto Bemporadalberto.bemporad@imtlucca.itKomei FukudaFabio Danilo Torrisi