Algorithmic geometry with infinite time computation
Document typeMaster thesis
Rights accessOpen Access
In 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.
DegreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)