{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/87694"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/87694","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Fast geometric algorithms","abstract":"This thesis addresses a number of important problems which fall within the framework of the new discipline of Computational Geometry. The list of topics covered includes sorting and selection, convex hull algorithms, the L₁ hull, determination of the minimum encasing rectangle of a set of points, the Euclidean and L₁ diameter of a set of points, the metric traveling salesman problem, and finding the superrange of starshaped and monotone polygons. The main theme of all our work has been to develop a set of very fast state-of-the-art algorithms which supercede any rivals in terms of speed and ease of implementation. 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