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Variants of Petersen coloring for some graph classes
Bílková, Hana ; Šámal, Robert (advisor) ; Rollová, Edita (referee)
Normal coloring - an equivalent version of Petersen coloring - is a special proper 5-edge-coloring of cubic graphs. Every edge in a normally colored graph is normal, i.e. it uses together with its four neighbours either only three colors or all five colors. Jaeger conjectured that every bridgeless cubic graph has a normal coloring. This conjecture, if true, imply for example Cycle double cover conjecture. Here we solve a weakened version of Jaeger's problem. We are looking for a proper 5-edge-coloring such that at least a part of the edges is normal. We show a coloring of generalized prisms with two thirds of the edges normal and a coloring of graphs without short cycles with almost half of the edges normal. Then we propose a new approach to normal coloring - chains. We use chains to prove that there cannot be only one single mistake in an almost normally colored graph. We also prove some statements about cuts in a normally colored graph which also follow from nowhere-zero Petersen flow. Finally, we examine a four-cycle in a normally colored graph. 1
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An iOS implementation of the Shannon switching game
Macík, Miroslav ; Vidová Hladká, Barbora (advisor) ; Hana, Jiří (referee)
Shannon switching game is a logical graph game for two players. The game was created by American mathematician Claude Shannon. iOS is an operating system designed for iPhone cellular phone, iPod music player and iPad tablet. The thesis describes existing implementations of the game and also specific implementation for iOS operating system created as a part of this work. This implementation allows you to play against virtual opponent and also supports multiplayer game consisting of two players playing on the same device or through the Internet against each other. Another component of the thesis is deep insight of algorithms describing next move decisions of virtual opponent or the techniques of game plan generation.
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Petersen coloring and variants
Bílková, Hana ; Šámal, Robert (advisor) ; Dvořák, Zdeněk (referee)
The Petersen coloring of 3-regular graph G is equivalent to the normal coloring by five colors. The normal coloring is a good coloring of edges such that every edge and its four neighbours have together three or five different colors. Jaeger conjectures that every bridgeless 3-regular graph has a Petersen coloring. If the conjecture were true, it would imply other interesting statements about 3-regular graphs. In this text we investigate normal coloring by more than five colors. Jaeger theorem about nowhere-zero Z2 3 -flow implies that every bridgeless graph has normal coloring by seven colors. Independently on the Jaeger theorem, we prove the existence of normal coloring by nine colors for graphs with a bridge, a cut of size two or with a triangle. The idea of our proof comes from Andersen's proof of existence of strong coloring by ten colors for 3-regular graphs. Finally, we sketch the idea of the proof for other classes of 3-regular graphs. 1
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An iOS implementation of the Shannon switching game
Macík, Miroslav ; Vidová Hladká, Barbora (advisor) ; Brom, Cyril (referee)
Shannon switching game is a two player logical game. The main principle is a graph and its two marked nodes. The first player's goal is to connect these two nodes without being stopped by the other player. Otherwise the second player needs to prevent the first one from connecting them in order to win. This game was created by an American mathematician Claude Shannon. Independently of him David Gale created a very same one, called Bridg-It or Gale. iOS is an operating system created by Apple Inc. company. This system is designed for iPhone mobile phones, iPod music players and iPad tablets. The base for developing this operating system is the Objective-C programming language and Cocoa Touch framework.
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Coevolutionary Algorithms Statistical Analysis Tool
Urban, Daniel ; Zachariášová, Marcela (referee) ; Drahošová, Michaela (advisor)
This bachelor thesis contains a theoretical basis that introduces evolutionary algorithms, genetic programming, coevolutioanary algorithms and methods for statistical evaluation. Furthermore, this work deals with the design and implementation of tool with graphical user interface, which allows the analysis of coevolutioanary algorithm for various parameters and also its statistical evaluation. The functionality of the implemented tool has been tested on data obtained from an external program performing evolutionary design of image filters with the use of the coevolution of tness predictors. The resulting graphs and statistics allow easy comparison of the progress and results for each program run.
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Analysis and Aggregation of Czech Parliament Data
Talašová, Irena ; Burget, Radek (referee) ; Očenášek, Pavel (advisor)
The aim of this work is to create a variety of statistics and reports on the functioning of Parliament of Czech Republic. Data for these statistics are gathered from the pages of the Czech Parliament and stored in to a database. Results are presented mainly in the form of tables, graphs and other methods on a publicly accessible Web site. Results should be as clear as possible, comprehensible and provide interesting and unusual information.
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Signal processing using parallel mathematical operations
Polášek, Jaromír ; Ležák, Petr (referee) ; Mžourek, Zdeněk (advisor)
This Bachelor thesis deals with the acceleration of function calculations, using parallel computing mediated by NVDIA graphics cards via CUDA technology. The theoretical part describes the general principles of parallel computing and the basic characteristics and parameters of graphics cards NVDIA. The theoretical part also deals with basic principles of CUDA technology. End of the theoretical part focuses on FFTW and cuFFT libraries. The practical part deals with the comparison of the performance between GPU and CPU functions filter2D and Canny and practical possibilities of accelerating fast convolution calculation. The practical part also describes sample code that was used to compare the performance between GPU and CPU. The results of this program are then plotted and evaluated.
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Visualization of multidimensional data using web technologies
Burian, Vojtěch ; Galáž, Zoltán (referee) ; Mžourek, Zdeněk (advisor)
Scope of this work is the problematic of data visualization. Data visualization is a useful tool to present and gather new information and thus get to better decisions. In theoretical part, data analysis topics are dealt with. Then specific types of graphs are listed and explained, and in next part problems with graph creation are pinpointed. Basics of graphic and web design are also mentioned. Practical part is focused on visualization of data of processed results of speech analysis, gathered from patients with Parkinson disease. Because majority of people in medical industry do not have, or is not able to work with specialized software (such as Matlab), outputs in HTML table and SVG format were created based on Python programming language. Both these parts are accommodated into webpage, which can be easily opened in web browser installed in most of computers regardless of operation system used.
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Public Tenders in EU: Statistics and Overview
Kurka, Vojtěch ; Trchalík, Roman (referee) ; Očenášek, Pavel (advisor)
The purpose of this bachelor thesis is to provide well-arranged statistics and surveys about tenders in the European Union. Statistics and surveys are visualized as graphs, textual informations and different kinds of maps. Those statistics are based on data from corresponding EU information system and stored in MySQL database. In advance these data are offered to others in machine readable format. Easy understanding and mainly graphical representation of data is the most important part. All statistics are accessible via web pages optimized for the most common web browsers.
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