Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
How good are convex hull algorithms?
Computational Geometry: Theory and Applications
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
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Given a set of polyhedral cones C"1,...,C"k@?R^d, and a convex set D, does the union of these cones cover the set D? In this paper we consider the computational complexity of this problem for various cases such as whether the cones are defined by extreme rays or facets, and whether D is the entire R^d or a given linear subspace R^t. As a consequence, we show that it is coNP-complete to decide if the union of a given set of convex polytopes is convex, thus answering a question of Bemporad, Fukuda and Torrisi.