Convexity recognition of the union of polyhedra

Bemporad, Alberto and Fukuda, Komei and Torrisi, Fabio Danilo Convexity recognition of the union of polyhedra. Computational Geometry, 18 (3). pp. 141-154. ISSN 0925-7721 (2001)

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Abstract

In 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.

Item Type: Article 10.1016/S0925-7721(01)00004-9 Polyhedron; Union; Convexity Q Science > QA Mathematics Computer Science and Applications Professor Alberto Bemporad 27 Jul 2011 09:32 17 Jul 2014 12:39 http://eprints.imtlucca.it/id/eprint/468