dc.contributor.author | Hu, Nan | |
dc.date.accessioned | 2013-08-15 15:52:27 (GMT) | |
dc.date.available | 2013-08-15 15:52:27 (GMT) | |
dc.date.issued | 2013-08-15T15:52:27Z | |
dc.date.submitted | 2013 | |
dc.identifier.uri | http://hdl.handle.net/10012/7703 | |
dc.description.abstract | 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 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.language.iso | en | en |
dc.publisher | University of Waterloo | en |
dc.subject | computational geometry | en |
dc.subject | approximation algorithm | en |
dc.subject | PTAS | en |
dc.subject | Red-Blue Set Cover | en |
dc.subject | Depth-(<K) Packing | en |
dc.subject | Disjoint Unit-Disk Cover | en |
dc.title | Approximation Algorithms for Geometric Covering Problems for Disks and Squares | en |
dc.type | Master Thesis | en |
dc.pending | false | en |
dc.subject.program | Computer Science | en |
uws-etd.degree.department | School of Computer Science | en |
uws-etd.degree | Master of Mathematics | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Unreviewed | en |
uws.scholarLevel | Graduate | en |