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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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Graphs, Algorithms and their Application
Venerová, Lenka ; Dostál,, Jiří (referee) ; Bobalová, Martina (advisor)
The Bachelor thesis is primarily focused on the problems of graphs and graph algorithms. The main point is to explain and to enlarge the subject. Very often, we find ourselves confronted with problems, which we, though unconsciously, solve by means of the graph algorithms knowledge. Therefore, the other aim of my bachelor thesis is to demonstrate the application of some of these methods in solving distribution tasks.
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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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Application of neural networks in telecommunications
Šulák, Michal ; Koula, Ivan (referee) ; Kacálek, Jan (advisor)
This Master’s Thesis consists of description of current routing protocols and routers, basic principles of neural networks and their interpretation in connection with the use for routing in data networks and telecommunications networks. In the thesis I focused on neural networks, which use energetic functions to find solution stabled states and their use for data routing. I produced the application software to test and find suitable variables for each function. This application counts the shortest path and is able to change variables to reach the best solution of stabled state of neural network. These solutions are compared with other functions that are usually used in nowadays systems for data network routing.
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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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Methods for Coloring Nodes in Multigraf
Knotek, Martin ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This thesis deals with algorithms for verticies coloring and their application to the coloring elements of electrical low voltage grid. Result of this thesis is a program, which displays progress of coloring five implemented algorithms on a selected graph. The graph represents electricity distribution network in a city.
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Graphics Graph Representation
Matula, Radek ; Goldefus, Filip (referee) ; Masopust, Tomáš (advisor)
This Master Thesis deals with the drawing algorithms of graphs known from the mathematical theory. These algorithms deals with an appropriate distribution of the graph vertices in order to obtain the most clear and readable graphs for human readers. The main objective of this work was also to implement the drawing algorithm in the application that would allow to edit the graph. This work deals also with graphs representation in computers.
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Constraint Satisfaction Problem and Universal Algebra
Kazda, Alexandr ; Barto, Libor (advisor) ; Růžička, Pavel (referee) ; Valeriote, Matt (referee)
The thesis consists of a collection of my contributions to universal algebra. Motivated by the Constraint Satisfaction Problem (CSP), we study the algebras of polymorphisms of relational structures. We begin by showing by an algebraic argument (and a bit of calculus) that random relational structures' CSP is almost always NP-complete. We then study digraphs with a Maltsev polymorphism, and conclude that such digraphs must also have a majority polymorphism. Next, we show how to use absorption tech- niques to prove that congruence modular reflexive digraphs must have an NU operation. We close our work by giving an algebraic proof of a result (first obtained by graph theorists) that 3-conservative relational structures with only unary and binary relations either define NP-complete CSP, or CSP for them can be solved by the local consistency algorithm. 1
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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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