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dc.contributor.authorHu, Nan 15:52:27 (GMT) 15:52:27 (GMT)
dc.description.abstractGeometric covering is a well-studied topic in computational geometry. We study three covering problems: Disjoint Unit-Disk Cover, Depth-(≤ K) Packing and Red-Blue Unit-Square 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 approximation scheme (PTAS) for it. In Depth-(≤ K) Packing for Arbitrary-Size Disks/Squares, we are given a set of arbitrary-size disks/squares, and want to find a subset with depth at most K and maximizing the total area. We prove a depth reduction theorem and present a PTAS. In Red-Blue Unit-Square Cover, we are given a red point set, a blue point set and a set of unit squares, and want to find a subset of unit squares to cover all the blue points and the minimum number of red points. We prove that the problem is NP-hard, and give a PTAS for it. A "mod-one" trick we introduce can be applied to several other covering problems on unit squares.en
dc.publisherUniversity of Waterlooen
dc.subjectcomputational geometryen
dc.subjectapproximation algorithmen
dc.subjectRed-Blue Set Coveren
dc.subjectDepth-(<K) Packingen
dc.subjectDisjoint Unit-Disk Coveren
dc.titleApproximation Algorithms for Geometric Covering Problems for Disks and Squaresen
dc.typeMaster Thesisen
dc.subject.programComputer Scienceen of Computer Scienceen
uws-etd.degreeMaster of Mathematicsen

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