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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Worst case driver for Top trees
 Ondráček, Lukáš ; Majerech, Vladan (advisor) ; Fink, Jiří (referee)
A top tree data structure solves one of the most general variants of a well- studied dynamic trees problem consisting in maintenance of a tree along with some aggregated information on paths or in individual trees, possibly in a mutable way, under operations of inserting and removing edges. It provides a simple interface separated from both an internal top tree structure representing a hierarchical partitioning of the graph, and a driver ensuring its depth to be logarithmic, which has a crucial role for the efficiency of the data structure. The driver proposed in this thesis is based on biased trees, combining techniques used in the worst-case version of link/cut trees and in the amortized driver for top trees: An input forest is decomposed into heavy paths and interleaving vertices, all of them being represented by biased trees connected together to form exactly the top tree structure. The driver is meant to be a more efficient alternative to the originally proposed one, and a comparably efficient alternative to the driver proposed by Werneck; there is a room for their experimental comparison.
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Drawing polytopes in various dimensions
 Ondráček, Lukáš ; Šámal, Robert (advisor) ; Mareš, Martin (referee)
The thesis describes implementation of an application for drawing three- and multidimensional polytopes allowing their fluent rotation. The application Geometric Figures for Linux and Windows is written in the C language using the OpenGL library and it supports plug-ins written in the Python language. Iterated perspective projection and edges coloring according to their location is used. In addition, the application is able to generate the convex hull of a set of points, cut figures with hyperplanes, stellate figures, create geometrically dual polytopes and cut off parts of figures; all functions are independent to the number of dimensions of the polytopes. The application profits from its easy extensibility using modules and its code being open-source. Powered by TCPDF (www.tcpdf.org)
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4 Ondráček, Leon
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