TY  - JOUR
VL  - 18
Y1  - 2001/04//
JF  - Computational Geometry
IS  - 3
A1  - Bemporad, Alberto
A1  - Fukuda, Komei
A1  - Torrisi, Fabio Danilo
PB  - Elsevier
SP  - 141
ID  - eprints468
EP  - 154
AV  - none
TI  - Convexity recognition of the union of polyhedra
KW  - Polyhedron; Union; Convexity
UR  - http://www.sciencedirect.com/science/article/pii/S0925772101000049
SN  - 0925-7721
N2  - 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.
ER  -