Approximation algorithms for partial covering problems
نویسندگان
چکیده
منابع مشابه
Approximation Algorithms for Partial Covering Problems
We study a generalization of covering problems called partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-partial set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-partial set cover, if each element occurs in at most f sets, then we derive a primal...
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Packing and Covering problems together capture many important problems in combinatorial optimization. We will consider covering problems in these notes. Two canonical covering problems are Vertex Cover and its generalization Set Cover. They play an important role in the study of approximation algorithms. A vertex cover of a graph G = (V,E) is a set S ⊆ V such that for each edge e ∈ E, at least ...
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Geometric covering is a well-studied topic in computational geometry. We study three covering problems: Disjoint Unit-Disk Cover, Depth-(≤ K) Packing and Red-Blue UnitSquare Cover. In the Disjoint Unit-Disk Cover problem, we are given a point set and want to cover the maximum number of points using disjoint unit disks. We prove that the problem is NP-complete and give a polynomial-time approxim...
متن کاملApproximation Algorithms for Partial Covering Problems (submission to Icalp 2001, Track A)
We study the generalization of covering problems to partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example , in k-set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-set cover, if each element occurs in at most f sets, then we derive a primal-dual f-approxima...
متن کاملApproximation Algorithms for Covering Polygons with Squares and Similar Problems
We consider the problem of covering polygons, without any acute interior angles, using a preferably minimum number of squares. The squares must lie entirely within the polygon. Let P be an arbitrary input polygon, with n vertices, coverable by squares. Let (P) denote the minimum number of squares required to cover P. In the rst part of this paper we show an O(n log n+(P)) time algorithm which p...
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ژورنال
عنوان ژورنال: Journal of Algorithms
سال: 2004
ISSN: 0196-6774
DOI: 10.1016/j.jalgor.2004.04.002