Minimal length of a travelling salesman's problem had been studied in this diploma these. Travelling salesman must come trough each place just once and then go back to the starting place. This problem can be illustrated as a problem of graph theory, such that places are the vertices, roads are the edges, distances of roads are the lengths of edges. The optimal travelling salesman's problem tour is the shortest Hamiltionian cycle in the graph. It is a classical NP-complete problem. There is no algorithm that solves this problem in polynomial time. This problem can be solved by using various approximation algorithms, they offer less time consumption and lowest quality than optimization. This diploma these had been dedicated to approximation algorithms, for example: nearest neighbor method, minimal spanning tree method, Christofide's method, 2-opt., genetic algorithm, etc.

The media play an indisputable role in human life. Thus, we come across media communication daily in today's world. Online social networks have had a significant role in such communication over the past decade. The Facebook social network presents an example of such a phenomenon, which does not have a rival in terms of its size in the Czech Republic. It has rapidly become a communication media through which millions of people around the world consume various content. In recent years, this platform has been applying and continually adjusting its algorithm to provide users with personalized content. The personalized content is provided on the basis of the algorithm which evaluates what might be appropriate or interesting for people. From this point of view, this thesis called Filter bubbles on Facebook social network is examining the existence of a so-called filter bubble phenomenon. The information bubbles present information isolation in which people lack a diversity of information which would help people to get into an opinion diversification, and therefore to have an opportunity to have a new point of view about a certain phenomenon. Through the combined qualitative method of diaries and subsequent interviews, it explores how young people consume news content on this social network and, above...

Grafické modely jsou vhodným nástrojem statistické analýzy. V poslední době byly aplikovány rovněž ve financích. Práce pojednává o grafických modelech určených pro zpracování dat pocházejících z normálního rozdělení. Jsou zde popsány možnosti testování shody modelů s daty a čtyři selekční algoritmy (včetně odvození vztahů mezi různými STOP pravidly) pro výběr vhodného grafu, který dobře reprezentuje konkrétní data. Tyto dosud nepříliš známé postupy jsou pak použity k zodpovězení otázek z oblasti českého i mezinárodního kapitálového trhu (zkoumání provázanosti odvětvových indexů BCPP, globalizace světových akciových trhů, provázanosti měnových kurzů) a rovněž k testování hypotéz pro vysvětlení časové struktury úrokových sazeb v České republice. Vytvořené programy ve formátu Mathematica 4 lze nalézt v příloze.

Současné konkurenční prostředí nutí distribuční firmy zajišťovat bezprostřední obsluhu svých zákazníků. Zatímco statická verze okružních a rozvozních úloh nepřipouští možnost akceptovat dodatečné požadavky zákazníků, dynamická verze umožňuje dispečerovi měnit naplánované trasy vozidel, jakmile se objeví nový požadavek. Pro řešení dynamických úloh jsou navrženy optimalizační matematické modely a heuristické vkládací algoritmy. V některých úlohách jsou zahrnuty podmínky s časovými okny. V práci jsou analyzovány speciální distribuční úlohy: dynamická úloha kurýrní služby, dynamická úloha obchodního cestujícího s apriorní informací a dynamická rozvozní úloha s dělenou dodávkou. Řešení většiny úloh je demonstrováno na vygenerovaných datech za použití programu LINGO jako řešitele a VBA v MS Excel jako uživatelského rozhraní a výstupního prostředí. Jsou prezentovány výsledky počítačových experimentů.

Title: Flows and cuts with constraints Author: Dušan Knop Department: Department of applied mathematics Supervisor: Doc. Mgr. Petr Kolman, PhD, Department of applied mathematics Abstract: In this thesis we study the problem of length bounded cuts between two vertices of a graph. In this problem the task is to find a set of edges such that after its removal the minimal distance between the two vertices is as prescribed. The work provides a basic overview of the literature on this problem and presents it in the context of other theoretical problems. It also offers some applications of length bounded cuts and flows. We describe some heuristics for data reduction. The main result of this thesis is a polynomial time algorithm in series-parallel graphs for problem of length bounded cut, which is NP-hard in general. Keywords: cuts, series-parallel graphs, algorithm, complexity

Suffix tree is a data structure which enables the performing of fast search-like operations on the text. In order to be used efficiently, it must be created quickly. In this thesis, we focus on the new kind of suffix link simulation called "minimized branching", which aims to increase the speed of suffix tree construction by reducing the number of branching operations. Our main goal is to present a comparison of the currently used methods for the suffix tree construction and to point out some advantages and disadvantages of the individual approaches. We introduce, implement and practically evaluate multiple variations of the standard McCreight's and Ukkonen's algorithms, as well as Partition and Write Only Top Down (PWOTD) algorithm, originally developed for disk-based construction. Our main result is the integrated description and implementation of these algorithms, which are both well-suited to be further built upon. We also present a simple recommendations on when it is advisable to use a particular algorithm's variation and why.

The thesis deals with algorithms for detecting anomalies in the data collected by the Problem Solving Tutor research. In the theoretical part, the author introduces the term of anomaly, the ideas of the PROSO research and a detailed overview of existing algorithms to detect anomalies. In the practical part, selected algorithms are implemented. Real outputs and results as well as recommendations to a user are presented in this part, and the chapter is supplemented by a number of graphs. The implemented algorithms are also compared to existing data mining software. An example of working with the data mining tools, applied to the data coming from PROSO, and explanation of their outputs is also part of the thesis. In the summary, the appropriate methodology for behavior analysis and anomaly detection is determinied.

This Master's thesis focuses on the area of pallet loading problem. It compares qualities of solutions generated by genetic algorithm to 5-block heuristics. Based on obtained information it focuses mainly on the stability of the distribution of boxes on a pallet. As a part of the thesis a testing environment was implemented with algorithms aforementioned.

This thesis deals with the adjustment of the current distribution routes of the company CHEMIE STAR Ltd. and at the same time with a creating of new distribution routes with the aim of economic savings, which is achieved through a reduction in the length of routes and the time required for the routes. In the introductory theoretical part of the work the logistics is defined, its functions, importance and influence on the enterprise. And this part also provides an overview of methods dealing with the traveling salesman problem. In the practical part the optimization of the input data into the model at the current routes is performed, where there is always selected the cheapest route between the two nodes using unit costs. Subsequently, the methods solving the traveling salesman problem are applied, namely the method of the Nearest neighbor, Vogel approximation method and Clark-Wright method. The layout of the new routes, which is limited in capacity by car and the purchasers requirements, is done using Mayer method and Sweep algorithm and with the subsequent application of the method solving the problem of traveling salesman problem. In the chapter evaluation of the results and recommendation all obtained outcomes are compared and interpreted.

In this thesis we study algorithmic aspects of balanced group presentations which are finite presentations with the same number of generators and relations. The main motivation is that the decidability of some problems, such as the triviality problem, is open for balanced presentations. First, we summarize known results on decision problems for general finite presen- tations and we show two group properties which are undecidable even for balanced presentations - the property of "being a free group"' and the property of "having a finite presentation with 12 generators". We also show reductions of some graph problems to the triviality problem for group presentations, such as determining whether a graph is connected, k-connected or connected including an odd cycle. Then we show a reduction of the determining whether a graph with the same number of vertices and edges is a cycle to the triviality problem for balanced presentations. On the other hand, there is also a limitation of reduction to balanced presentations. We prove that there is no balanced presentation with two generators a, b|ap(m) bq(m) , ar(m) bs(m) for p(m), q(m), r(m), s(m) ∈ Z[m] which describes the trivial group if and only if m is odd. In the last part of this thesis, we describe a relation between group presentations and topology. In addition,...