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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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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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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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