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Graphs and Shortest Path Algorithms
Hamerník, Michal ; Nowák, Jiří (referee) ; Bobalová, Martina (advisor)
This bachelor thesis represents an educational text focused on graph theory and graph algorithms. The graph theory often helps to solve problems between parts of a complicated unit and graph algorithms are quick and effective in their optimization. Basics of graph theory, samples of graph algorithms and practical examples of use are described in it. This thesis can be used as a supplementary text in Discrete Mathematics taught at Faculty of Business and Management in Brno University of Technology.
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The Shortest Graph's Pahts Finding
Jágr, Petr ; Ohlídal, Miloš (referee) ; Jaroš, Jiří (advisor)
The aim of this thesis is finding, comparing and implementation of algorithms for finding the shortest paths between each of pairs of nodes in a graph. For this task I use modifications of existing algorithms to achive the lowest time consumption of the computation. Modifications are established on Dijkstra's and Floyd-Warshall's algorithm. We also familiarize with Bellman-Ford algorithm.
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Shopping Advisor
Kocourek, Jakub ; Bartík, Vladimír (referee) ; Kolář, Dušan (advisor)
The attached bachelor thesis deals with nding the shortest ways in a shop for the selected purchase. The different technologies of creating web pages are described. As for the state space search algorithms are given for nding the shortest path between two points and for solving the travel salesmen problem. The thesis continues with the description of a design and implementation of application with all used technologies (PHP, Nette, MySQL, JS, JQuery) applying the Dijkstra's algorithm for nding the shortest path and genetic algorithm for solving the travel salesmen problem.
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Demonstration of Graph Algorithms
Varadinek, Jakub ; Zámečníková, Eva (referee) ; Křivka, Zbyněk (advisor)
This bachelor thesis deals with the development of the application for demonstration and visualization of several graph algorithms. The application allows the user to create a graph, rate edges or name and layout vertices. The individual algorithms can be performed in created graph for visual observation how the algorithm works. There is also the possibility of stepping through the chosen algorithm and an interactive mode where next steps are selected by the user and the application checks the correctness of these steps.
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Shortest Paths in a Graph
Krauter, Michal ; Křivka, Zbyněk (referee) ; Masopust, Tomáš (advisor)
This thesis deals with shortest paths problem in graphs. Shortest paths problem is the basic issue of graph theory with many pracitcal applications. We can divide this problem into two following generalizations: single-source shortest path problem and all-pairs shortest paths problem. This text introduces principles and algorithms for generalizations. We describe both classical and new more efficient methods. It contains information about how some of these algorithms were implemented and offers an experimental comparison of these algorithms.
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Mobile Robot Navigation
Goldmann, Tomáš ; Luža, Radim (referee) ; Orság, Filip (advisor)
When we look at the eld of robotics we nd that exist a lot of types of robots. Some of tham use location navigation and global navigation for their work. This work aims to map options of location navigation and description of basic technique which used. Especially, we will deal with algorithms which work with optical sensors, for example camera, stereocamera or laser which scan medium. Practise section this work is focused on the proposal and implementacion algorithm which working with local navigation for robot's return to the starting position. All this work is connecting with tracked robot which formed in the framework one of project realization at Faculty of information technology.
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Analysis of Data Flow in the Fly-by-Wire System
Kubínová, Zuzana ; Tomáš, Jan (referee) ; Matoušek, Radomil (advisor)
Software implementovaný v rámci Fly-by-Wire systému firmy Honeywell je složen z mnoha modelů implementovaných v systému Simulink. Tato práce se zabývá hledáním přímých a nepřímých spojitostí mezi jednotlivými signály v systému těchto modelů. Jako vhodný aparát je zvolena teorie grafů. Na základě modelů jsou vygenerovány grafy a úloha nalézt spojitost mezi signály je převedena na úlohu nalézt cestu mezi dvěma vrcholy grafu. Známé algoritmy k vyhledávání cest v grafech určují délku nebo váhu nalezené cesty. Pro tuto aplikaci je ale potřeba rozlišovat cesty primární a sekundární bez ohledu na jejich délku. Proto jsou tyto známé algoritmy upraveny.
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