Notes on Convex Transversals
نویسنده
چکیده
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.
منابع مشابه
The Intersection of Convex Transversals is a Convex Polytope
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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INTRODUCTION Let F be a family of convex sets in R. A geometric transversal is an affine subspace that intersects every member of F . More specifically, for a given integer 0 ≤ k < d, a k-dimensional affine subspace that intersects every member of F is called a ktransversal to F . Typically, we are interested in necessary and sufficient conditions that guarantee the existence of a k-transversal...
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ورودعنوان ژورنال:
- CoRR
دوره abs/1211.5107 شماره
صفحات -
تاریخ انتشار 2012