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dc.contributorMuller, Moritz Martin
dc.contributorHuemer, Clemens
dc.contributor.authorTobar Nicolau, Adrian
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2020-07-30T16:15:24Z
dc.date.available2020-07-30T16:15:24Z
dc.date.issued2020-07
dc.identifier.urihttp://hdl.handle.net/2117/328100
dc.description.abstractIn this project we do an algorithmic study of problems from computational geometry with countably infinite input, especially countable sets in R^n. To do so, we use the infinite time Blum-Shub-Smale (ITBSS) machine, which is capable to extend computations to infinite time. We present this framework, explained with several algorithms, some results on the ITBSS Machine, and a storage system capable of encoding, editing and extracting sequences of real numbers. We study different geometric problems, giving algorithmic solutions to several of them. The accumulation points problem in R^2 is presented and solved for countable sets with finitely many accumulation points. Also, the convex hull problem is studied. We show how to compute the closure of the convex hull of countable bounded sets in R^n. The non-crossing perfect matching problem with infinite input is addressed as well.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Informàtica
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshComputing Methodologies.
dc.subject.otherAlgorithms
dc.subject.otherInfinite Computation
dc.subject.otherInfinite input
dc.subject.otherInfinite Time
dc.subject.otherComputational Geometry
dc.subject.otherBlum-Shub-Smale
dc.subject.otherAccumulation point
dc.subject.otherConvex Hull
dc.subject.otherMatching
dc.titleAlgorithmic geometry with infinite time computation
dc.typeMaster thesis
dc.subject.lemacInformàtica
dc.subject.amsClassificació AMS::68 Computer science::68U Computing methodologies and applications
dc.identifier.slugFME-2034
dc.rights.accessOpen Access
dc.date.updated2020-07-17T09:24:56Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)


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Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain