Geometric red–blue set cover for unit squares and related problems
نویسندگان
چکیده
منابع مشابه
Geometric Red-Blue Set Cover for Unit Squares and Related Problems
We study a geometric version of the Red-Blue Set Cover problem originally proposed by Carr, Doddi, Konjevod, and Marathe (SODA 2000): given a red point set, a blue point set, and a set of objects, we want to choose a subset of objects to cover all the blue points, while minimizing the number of red points covered. We prove that the problem is NP-hard even when the objects are unit squares in 2D...
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We study the Unique Set Cover problem on unit disks and unit squares. For a given set P of n points and a set D of m geometric objects both in the plane, the objective of the Unique Set Cover problem is to select a subset D′ ⊆ D of objects such that every point in P is covered by at least one object in D′ and the number of points covered uniquely is maximized, where a point is covered uniquely ...
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We study the planar version of Minimum-Weight Set Cover, where one has to cover a given set of points with a minimum-weight subset of a given set of planar objects. For the unit-weight case, one PTAS (on disks) is known. For arbitrary weights however, the problem appears much harder, and in particular no PTASs are known. We present the first PTAS for Weighted Geometric Set Cover on planar objec...
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We study several set cover problems in low dimensional geometric settings. Specifically, we describe a PTAS for the problem of computing a minimum cover of given points by a set of weighted fat objects. Here, we allow the objects to expand by some prespecified δ-fraction of their diameter. Next, we show that the problem of computing a minimum weight cover of points by weighted halfplanes (witho...
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Given an instance of a geometric set cover problem on a set of points X and a set of objects R, the dual is a geometric hitting set problem on a set of points P and a set of objects Q, where there exists a one-to-one mapping from each xj ∈ X to a dual object Qj ∈ Q and for each Ri ∈ R to a dual point in pi ∈ P , so that a dual point pi is contained in a dual object Qj if and only if the corresp...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2015
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2014.12.005