Convex transversals
نویسندگان
چکیده
منابع مشابه
Convex Transversals
We answer the question initially posed by Arik Tamir at the Fourth NYU Computational Geometry Day (March, 1987): “Given a collection of compact sets, can one decide in polynomial time whether there exists a convex body whose boundary intersects every set in the collection?” We prove that when the sets are segments in the plane, deciding existence of the convex stabber is NP-hard. The problem re...
متن کاملNotes on Convex Transversals
In this paper, we prove the problem of stabbing a set of disjoint bends by a convex stabber to be NP-hard. We also consider the optimization version of the convex stabber problem and prove this problem to be APX-hard for sets of line segments.
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R d can be divided into a union of parallel d k ats of the form x g x g xk gk where the gi are constant Let C be a family of parallel d k dimensional convex sets meaning that each is contained in one of the above parallel d k ats We give a parameterization of the set of k ats in R such that the set of k ats which intersect in a point any set c C is convex Parameterizing the lines in R through h...
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We establish a bound of O(nk), for any ε > 0, on the combinatorial complexity of the setT of line transversals of a collection P of k convex polyhedra in R with a total of n facets, andpresent a randomized algorithm which computes the boundary of T in comparable expectedtime. Thus, when k ¿ n, the new bounds on the complexity (and construction cost) of Timprove upon the previous...
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It is proven that the intersection of convex transversals of finitely many sets in R is a convex polytope, possibly empty. Related results on support hyperplanes and complements of finite unions of convex sets are given. MSC 2000: 52A20
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2014
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2012.10.009