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Nekonečné matroidy
Böhm, Martin ; Pangrác, Ondřej (advisor) ; Loebl, Martin (referee)
We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)
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Graph labeling
Böhm, Martin ; Mareš, Martin (advisor) ; Balyo, Tomáš (referee)
We introduce the concept of adjacency labeling schemes and recent results in the area. These schemes have practical application in parallel algorithm design and they relate to the theory of universal graphs. We concentrate on the modern technique of "Traversal and Jumping". We present a less technical proof of its correctness as well as correcting some errors in the original proof. We also apply brute-force algorithms to find small induced-universal graphs. 1
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Post-processing of scanned documents
Tichý, Jan ; Mareš, Martin (advisor) ; Böhm, Martin (referee)
The subject of this work is to propose a method for post-processing of scanned documents containing text and non-text elements. In this work, this problem is analyzed and divided into smaller sub- problems, which are solved. Main problems we propose solutions to are pre-processing of an input image to suppress scanning defects such as poor contrast or rotation of an input image, segmentation to characters, lines and images and finally compression of output document by clustering text elements. We will implement this proposed method as a program processing scanned images into PDF document. Powered by TCPDF (www.tcpdf.org)
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Online Bin Stretching: Algorithms and Computer Lower Bounds
Böhm, Martin ; Sgall, Jiří (advisor) ; Durr, Christoph (referee) ; Kellerer, Hans (referee)
Online Bin Stretching: Algorithms and Computer Lower Bounds Author: Martin Böhm Abstract: We investigate a problem in semi-online algorithm design, called Online Bin Stretching. The problem can be understood as an online repacking problem: the goal of the algorithm is to repack items of various sizes into m containers of identical size R > 1. The input items arrive one by one and the algorithm must assign an item to a container before the next item arrives. A specialty of this problem is that there is a specific guarantee made to the algorithm: the algorithm learns at the start of the input that there exists a packing of all input items into m containers of capacity 1. Our goal is to design algorithms for this problem which successfully pack the entire incoming sequence one by one while requiring the lowest container capacity R possible. In this thesis, we show several new results about Online Bin Stretching: First, we design an algorithm that is able to pack the entire input into m containers of capacity 1.5 regardless of what the vale of m will be. Second, we show a specialized algorithm for the setting of just 3 containers; this algorithm is able to pack into 3 bins of capacity 1.375. Finally, we design and implement an involved search algorithm which is able to find lower bounds for Online Bin...
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Walks in time-dymanic graph model
Beliš, Marek ; Pangrác, Ondřej (advisor) ; Böhm, Martin (referee)
Orienteering with moving control points can be represented as a graph model with ranked vertices and oriented edges. The rank of vertex depends on the actual time. Searching for the most optimised walk through this graph is exponentially difficult problem which can be in real-time solved only with limiting conditions and using of heuristics. SMIK solver software provides implemented heuristics for searching the best walk in several ways. In the thesis we can find description of the problem and algorithms, programming documentation with description of used methods and comparation of results to the real competition. Powered by TCPDF (www.tcpdf.org)
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Walks in time-dymanic graph model
Beliš, Marek ; Pangrác, Ondřej (advisor) ; Böhm, Martin (referee)
Orienteering with moving control points can be represented as a graph model with ranked vertices and oriented edges. The rank of vertex depends on the actual time. Searching for the most optimised walk through this graph is exponentially difficult problem which can be in real-time solved only with limiting conditions and using of heuristics. SMIK solver software provides implemented heuristics for searching the best walk in several ways. In the thesis we can find description of the problem and algorithms, programming documentation with description of used methods and comparation of results to the real competition. Powered by TCPDF (www.tcpdf.org)
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Post-processing of scanned documents
Tichý, Jan ; Mareš, Martin (advisor) ; Böhm, Martin (referee)
The subject of this work is to propose a method for post-processing of scanned documents containing text and non-text elements. In this work, this problem is analyzed and divided into smaller sub- problems, which are solved. Main problems we propose solutions to are pre-processing of an input image to suppress scanning defects such as poor contrast or rotation of an input image, segmentation to characters, lines and images and finally compression of output document by clustering text elements. We will implement this proposed method as a program processing scanned images into PDF document. Powered by TCPDF (www.tcpdf.org)
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Nekonečné matroidy
Böhm, Martin ; Pangrác, Ondřej (advisor) ; Loebl, Martin (referee)
We summarize and present recent results in the field of infinite matroid theory. We define and prove basic properties of infinite matroids and we discuss known classes of examples of these structures. We focus on the topic of connectivity of infinite matroids and we link some matroid properties to connectivity. The main result of this work is the proof of existence of infinite matroids with arbitrary finite connectivity, but without finite circuits or cocircuits. Powered by TCPDF (www.tcpdf.org)
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Graph labeling
Böhm, Martin ; Mareš, Martin (advisor) ; Balyo, Tomáš (referee)
We introduce the concept of adjacency labeling schemes and recent results in the area. These schemes have practical application in parallel algorithm design and they relate to the theory of universal graphs. We concentrate on the modern technique of "Traversal and Jumping". We present a less technical proof of its correctness as well as correcting some errors in the original proof. We also apply brute-force algorithms to find small induced-universal graphs. 1
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The overview and the evaluation of the technical specifications of transparent materials for the production of composite wood panels
Holub, Jan ; Böhm, Martin (advisor) ; Arnetová, Karolína (referee)
Work includes: general introduction to the components of the wood-based panels with a transparent layer, the history of their production. It includes requirements for individual components of composite wood panels and requirements for wood and other wood-based materials, which serve as reinforcement. Also mentions claims potting material, which serves as a matrix.
It includes a description of the technology of wood-based panels with a transparent layer. This paper introduces the most commonly used material serving as a matrix, their distinctive characteristics essential for the production of composite plates. Compares parameters resins based on polyester, polyurethane and epoxy resins and analyzes the choice of a suitable material for producing a composite board based on user requirements. Part of this work is to design materials for the manufacture of composite board with controlled light distribution.
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