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We consider various hitting and piercing problems for the family of axis-parallel rectangles induced by a point set. Selection Lemmas on induced objects are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection Lemma type(More)
We say a family of geometric objects C has (l, k)-property if every subfamily C ⊆ C of cardinality at most l is k-piercable. In this paper we investigate the existence of g(k, d) such that if any family of objects C in R d has the (g(k, d), k)-property, then C is k-piercable. Danzer and Grünbaum showed that g(k, d) is infinite for families of boxes and(More)
Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically show that there exists a point that is contained in many objects that are induced (spanned) by an underlying point set. In(More)
Given a 1.5-dimensional terrain T , also known as an x-monotone polygonal chain, the Terrain Guarding problem seeks a set of points of minimum size on T that guards all of the points on T . Here, we say that a point p guards a point q if no point of the line segment pq is strictly below T . The Terrain Guarding problem has been extensively studied for over(More)
We investigate the parameterized complexity of Generalized Red Blue Set Cover (Gen-RBSC), a generalization of the classic Set Cover problem and the more recently studied Red Blue Set Cover problem. Given a universe U containing b blue elements and r red elements, positive integers $$k_\ell $$ k ℓ and $$k_r$$ k r , and a family $$\mathcal F $$ F of $$\ell $$(More)