Convexity recognition of the union of polyhedra

Authors:
Alberto Bemporad;Komei Fukuda;Fabio D. Torrisi
Affiliations:
Automatic Control Laboratory, ETHZ, ETL I 26 CH-8092 Zurich, Switzerland and Dipartimento di Engegneria dell'Informazione, Università di Siena, Via Roma 56, 53100 Siena, Italy;Institute for Operations Research, ETHZ, CLP D2 CH-8092 Zurich, Switzerland and Department of Mathematics, EPFL, CH-1015 Lausanne, Switzerland;Automatic Control Laboratory, ETHZ, ETL I 26 CH-8092 Zurich, Switzerland
Venue:
Computational Geometry: Theory and Applications
Year:
2001

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Abstract

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, 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.