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dc.contributor.advisorMitchell, Joseph S. B.en_US
dc.contributor.authorIwerks, Justin Giften_US
dc.contributor.otherDepartment of Applied Mathematics and Statisticsen_US
dc.date.accessioned2013-05-22T17:34:49Z
dc.date.available2013-05-22T17:34:49Z
dc.date.issued1-Aug-12en_US
dc.date.submitted12-Augen_US
dc.identifierIwerks_grad.sunysb_0771E_11012en_US
dc.identifier.urihttp://hdl.handle.net/1951/59700
dc.description127 pg.en_US
dc.description.abstractGeometric visibility is fundamental to computational geometry and its applications in areas such as robotics, sensor networks, CAD, and motion planning. We explore combinatorial and computational complexity problems arising in a collection of settings that depend on various notions of visibility. We first consider a generalized version of the classical art gallery problem in which the input specifies the number of reflex vertices r and convex vertices c of the simple polygon (n = r + c). This additional information better characterizes the shape of the polygon. Through a lower bound construction, tight combinatorial bounds for coverage are achieved for all r >=0 and c >= 3. The combinatorics of guarding polyominoes and other polyforms are studied in terms of m, the number of cells, as opposed to the traditional parameter n. Various visibility models and guard types are considered. We establish that finding a minimum cardinality guard set for covering a polyomino is NP-hard. We introduce an algorithm for constructing a spiral serpentine polygonization of a set of n >= 3 points in the plane. The algorithm's behavior can be viewed as incrementally appending a visible triangle to the triangulation constructed so far. We consider beacon-based point-to-point routing and coverage problems. A beacon b is a point that can be activated to effect a gravitational pull toward itself in a polygonal domain. Algorithms are given for computing the attraction region of b and finding a minimum size set of beacons to route from a source s to a destination t given a finite set of candidate beacon locations. We show that finding a minimum cardinality set of beacons to cover a simple polygon or conduct certain types of routing in a simple polygon is NP-hard.en_US
dc.description.sponsorshipStony Brook University Libraries. SBU Graduate School in Department of Applied Mathematics and Statistics. Charles Taber (Dean of Graduate School).en_US
dc.formatElectronic Resourceen_US
dc.language.isoen_USen_US
dc.publisherThe Graduate School, Stony Brook University: Stony Brook, NY.en_US
dc.subject.lcshApplied mathematics Ð Computer scienceen_US
dc.subject.otherAlgorithms, Art gallery theorem, Combinatorics, Computational complexity, Computational geometry, Visibility coverageen_US
dc.titleCombinatorics and complexity in geometric visibility problemsen_US
dc.typeDissertationen_US
dc.description.advisorAdvisor(s): Mitchell, Joseph S. B. . Committee Member(s): Mitchell, Joseph S. B.; Arkin, Esther M. Skiena, Steven; Gao, Jieen_US
dc.mimetypeApplication/PDFen_US


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