Improved Results on Geometric Hitting Set Problems
نویسندگان
چکیده
منابع مشابه
Improved Results on Geometric Hitting Set Problems
We consider the problem of computing minimum geometric hitting sets in which, given a set of geometric objects and a set of points, the goal is to compute the smallest subset of points that hit all geometric objects. The problem is known to be strongly NP-hard even for simple geometric objects like unit disks in the plane. Therefore, unless P=NP, it is not possible to get Fully Polynomial Time ...
متن کاملImproved Local Search for Geometric Hitting Set
Over the past several decades there has been steady progress towards the goal of polynomial-time approximation schemes (PTAS) for fundamental geometric combinatorial optimization problems. A foremost example is the geometric hitting set problem: given a set P of points and a set D of geometric objects, compute the minimum-sized subset of P that hits all objects in D. For the case where D is a s...
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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...
متن کاملGeometric Hitting Set and Set Cover Problem with Half-Strips
We show that hitting set and set cover problems with half-strips oriented in two opposite directions are NPcomplete.
متن کاملKernelization Algorithms for d-Hitting Set Problems
A kernelization algorithm for the 3-Hitting-Set problem is presented along with a general kernelization for d-Hitting-Set problems. For 3-Hitting-Set, a quadratic kernel is obtained by exploring properties of yes instances and employing what is known as crown reduction. Any 3-Hitting-Set instance is reduced into an equivalent instance that contains at most 5k + k elements (or vertices). This ke...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2010
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-010-9285-9