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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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Impact of graph structures' features on the behaviour of the choosen distributed algorithm
Daňhel, Tomáš ; Škorpil, Vladislav (referee) ; Kenyeres, Martin (advisor)
The goal of this thesis is to describe the effect of the graph structures’ properties on the behavior of the chosen distributed algorithm. In the first part, I have described the theoretical concept and the behavior of the distributed algorithms. In the next part, I have focused my attention on describing the mathematical tools used to analyze the distributed algorithm. In the second part, I have focused on a detailed description of average consensus and wireless sensor networks. In the last part, we have presented the results of the practical experiments.
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Impact of graph structures' features on the behaviour of the choosen distributed algorithm
Daňhel, Tomáš ; Škorpil, Vladislav (referee) ; Kenyeres, Martin (advisor)
The goal of this thesis is to describe the effect of the graph structures’ properties on the behavior of the chosen distributed algorithm. In the first part, I have described the theoretical concept and the behavior of the distributed algorithms. In the next part, I have focused my attention on describing the mathematical tools used to analyze the distributed algorithm. In the second part, I have focused on a detailed description of average consensus and wireless sensor networks. In the last part, we have presented the results of the practical experiments.
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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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Graph theory and its applications
Huclová, Alena ; Karásek, Jiří (referee) ; Pavlík, Jan (advisor)
It is often necessary to be oriented in the complicated relations between parts of a unit. This problem can be solved by the graphs’ theory very well. Graph G is an ordered pair (V,E) where V is a non-empty set of vertices (our parts of the unit) and E is a set of two-element subsets of the set V called arcs (i.e. relations between parts of the unit). G= (V,E) The graph aplication is frequently hidden. It is not found in the solution of the problem, but could be used to express and substantiate it quite easily. In my work I will deal with optimization problems of a graph. Problem of the maximum network flow that we solve using directed graph can be an example. As for non-directed graphs, we will be interested in the search of a minimum frame of a graph.
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