Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 204-208). Also available via the Internet.

M.Sc. / The aim of this thesis is to investigate the topic of edge-colourings of graphs in the context of hereditary graph properties. We particularly aim to investigate analogues of reducibility, unique factorization and some related concepts. Chapter 1 gives the basic definitions and terminology. A few useful general results are also stated. In Chapter 2 we define and investigate decomposability, the analogue of reducibility. Some general results are first proved, such as that the indecomposability of an additive induced-hereditary property in the lattice of such properties implies that it is indecomposable in a general sense. The decomposability of various specific properties is then investigated in the rest of the chapter. In Chapter 3 we investigate unique decomposability, the analogue of unique factorization. We give examples showing that not every additive hereditary property is uniquely decomposable, and we obtain some results on homomorphism properties which lead to the unique decomposability of Ok. We also consider some related questions, such as cancellation and preservation of strict inclusions. Chapter 4 deals with Ramsey properties. We obtain some general results and, using the so-called partite construction, we obtain a few restricted Ramsey-graph results. As a corollary, we obtain two more unique decomposability results. In Chapter 5 we obtain various bounds involving the property Vk of k-degeneracy. We also investigate the sharpness of these bounds and prove that Vk is indecomposable for every k. Chapter 6 deals with the connection between colourings of infinite graphs and properties of finite graphs. We obtain some extensions of the Compactness Principle and give an example showing that the Compactness Principle can be useful in studying finite graphs.

Ph.D. / Please refer to full text to view abstract

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In this dissertation we employ stack and queue layouts of graphs to explore the relative power of stacks and queues. Stack layout and queue layouts of graphs can be examined from several points of view. A stack or a queue layout of a graph can be thought of as an embedding of the graph in a plane satisfying certain constraints, or as a graph linearization that optimizes certain cost measures, or as a scheme to process the edges of the graph using the fewest number of stacks or queues. All three points of view permeate this research, though the third point of view dominates. Specific problems in stack and queue layouts of graphs have their origin in the areas of VLSI, fault-tolerant computing, scheduling parallel processes, sorting with a network of stacks and queues, and matrix computations. We first present two tools that are useful in the combinatorial and algorithmic analysis of stack and queue layouts as well as in determining bounds on the stacknumber and the queuenumber for a variety of graphs. The first tool is a formulation of a queue layout of a graph as a covering of its adjacent matrix with staircases. Not only does this formulation serve as a tool for analyzing stack and queue layouts, it also leads to efficient algorithms for several problems related to sequences, graph theory, and computational geometry. The connection between queue layouts and matrix covers also forms the basis of a new scheme for performing matrix computations on a data driven network. Our analysis reveals that this scheme uses less hardware and is faster than existing schemes. The second tool is obtained by considering separated and mingled layouts of graphs. This tool allows us to obtain lower bounds on the stacknumber and the queuenumber of a graph by partitioning the graph into subgraphs and simply concentrating on the interaction of the subgraphs. These tools are used to obtain results in three areas. The first area is stack and queue layouts of directed acyclic graphs (dags). This area is motivated by problems of scheduling parallel processes. We establish the stacknumber and the queuenumber of classes of dags such as trees, unicylic graphs, outerplanar graphs, and planar graphs. We then present linear time algorithms to recognize 1-stack dags and leveled-planar dags. In contrast, we show that the problem of recognizing 9-stack dags and the problem of recognizing 4-queue dags are both NP-complete. The second area is stack and queue layouts of partially ordered sets (posets). We establish upper bounds on the queuenumber of a poset in terms of other measures such as length, width, and jumpnumber. We also present lower bounds on the stacknumber and on the queuenumber of certain classes of posets. We conclude by showing that the problem of recognizing a 4-queue poset is NP-complete. The third area is queue layouts of planar graphs. While it has been shown that the stacknumber of the family of planar graphs is 4, the queuenumber of planar graphs is unknown. We conjecture that a family of planar graphs—the stellated triangles—has unbounded queuenumber; using separated and mingled layouts, we demonstrate significant progress towards that result. / Ph. D.

A busca por métodos de leitura biométrica tem crescido muito, alimentada pelas necessidades governamentais, militares e comerciais. Pesquisas indicam que o mercado de reconhecimento facial vai movimentar bilhões de dólares nos próximos anos. Dessa forma, encontrar métodos que atendem situações específicas impulsiona novos avanços nessa área. Cada aplicação de reconhecimento de faces precisa de uma solução particular. Há casos que o tempo de resposta é o fator mais importante; outros exigem que a face seja classificada mesmo que de forma parcial. Em todas essas situações, a acurácia e a robustez talvez sejam os atributos mais importantes. Entretanto, na maioria das vezes, tais características se comportam como grandezas inversas: aumentado o grau de confiança dos resultados o desempenho do método será afetado. Por isso, desenvolver uma metodologia que equilibra tais fatores é essencial para a construção de soluções aceitáveis. Este trabalho apresenta um novo algoritmo de reconhecimento facial, baseado em descritores locais e em redes complexas. O método é capaz de concentrar a informação, antes distribuída pelos diversos pontos dos descritores, em um único vetor de características, tornando a classificação mais rápida e eficiente. Além disso, o outro foco da metodologia é reduzir etapas de pré-processamento, evitando que processos sejam executados de forma desnecessária. Os experimentos foram realizados com bancos de faces bem conhecidos na literatura, revelando taxas de acurácia de até 98,5%. A técnica também apresentou bons resultados mesmo quando havia ruídos nas amostras, muitas vezes oriundos de objetos presentes na composição do cenário. Para uma análise complementar, algoritmos clássicos de reconhecimento facial foram submetidos ao mesmo conjunto de dados, gerando assim resultados comparativos entre as metodologias. / The search for biometric scanning methods has grown a lot due to government, military and commercial needs. Researches indicate the face recognition market will move billions of dollars in next years. Thus, finding methods to specific situations drives new advances in this area. Each application face recognition requires a particular solution. There are cases the response time is the most important factor; others require that face must be classified even if partially. In all these situations, accuracy and robustness may be the most important attributes. However, in most cases, these features behave as inverse greatness: increasing the confidence level of the results the method performance will be affected. Therefore, create the method which balances these factors is essential for construction of acceptable solutions. This paper presents a new face recognition algorithm based on local descriptors and complex networks. The method is able to concentrate the information before distributed by various point descriptors, in a unique feature vector. It makes the classification step faster and more efficient. Furthermore, another focus of the method is reduce pre-processing steps, avoiding unnecessary processes. The experiments were conducted with faces datasets well known in the literature, revealing accuracy rates of up to 98.5%. The technique also showed good results when there was noise in the samples, often derived from objects present in the composition of the scene. For additional analysis, classical facial recognition algorithms were subjected to the same data set, generating comparative results between both methodologies.

A busca por métodos de leitura biométrica tem crescido muito, alimentada pelas necessidades governamentais, militares e comerciais. Pesquisas indicam que o mercado de reconhecimento facial vai movimentar bilhões de dólares nos próximos anos. Dessa forma, encontrar métodos que atendem situações específicas impulsiona novos avanços nessa área. Cada aplicação de reconhecimento de faces precisa de uma solução particular. Há casos que o tempo de resposta é o fator mais importante; outros exigem que a face seja classificada mesmo que de forma parcial. Em todas essas situações, a acurácia e a robustez talvez sejam os atributos mais importantes. Entretanto, na maioria das vezes, tais características se comportam como grandezas inversas: aumentado o grau de confiança dos resultados o desempenho do método será afetado. Por isso, desenvolver uma metodologia que equilibra tais fatores é essencial para a construção de soluções aceitáveis. Este trabalho apresenta um novo algoritmo de reconhecimento facial, baseado em descritores locais e em redes complexas. O método é capaz de concentrar a informação, antes distribuída pelos diversos pontos dos descritores, em um único vetor de características, tornando a classificação mais rápida e eficiente. Além disso, o outro foco da metodologia é reduzir etapas de pré-processamento, evitando que processos sejam executados de forma desnecessária. Os experimentos foram realizados com bancos de faces bem conhecidos na literatura, revelando taxas de acurácia de até 98,5%. A técnica também apresentou bons resultados mesmo quando havia ruídos nas amostras, muitas vezes oriundos de objetos presentes na composição do cenário. Para uma análise complementar, algoritmos clássicos de reconhecimento facial foram submetidos ao mesmo conjunto de dados, gerando assim resultados comparativos entre as metodologias. / The search for biometric scanning methods has grown a lot due to government, military and commercial needs. Researches indicate the face recognition market will move billions of dollars in next years. Thus, finding methods to specific situations drives new advances in this area. Each application face recognition requires a particular solution. There are cases the response time is the most important factor; others require that face must be classified even if partially. In all these situations, accuracy and robustness may be the most important attributes. However, in most cases, these features behave as inverse greatness: increasing the confidence level of the results the method performance will be affected. Therefore, create the method which balances these factors is essential for construction of acceptable solutions. This paper presents a new face recognition algorithm based on local descriptors and complex networks. The method is able to concentrate the information before distributed by various point descriptors, in a unique feature vector. It makes the classification step faster and more efficient. Furthermore, another focus of the method is reduce pre-processing steps, avoiding unnecessary processes. The experiments were conducted with faces datasets well known in the literature, revealing accuracy rates of up to 98.5%. The technique also showed good results when there was noise in the samples, often derived from objects present in the composition of the scene. For additional analysis, classical facial recognition algorithms were subjected to the same data set, generating comparative results between both methodologies.

Title: Algebraic, Structural and Complexity Aspects of Geometric Representations of Graphs Author: Peter Zeman Department: Computer Science Institute Supervisor: RNDr. Pavel Klavík Supervisor's e-mail: klavik@iuuk.mff.cuni.cz Keywords: automorphism groups, interval graphs, circle graphs, comparability graphs, H-graphs, recognition, dominating set, graph isomorphism, maximum clique, coloring Abstract: We study symmetries of geometrically represented graphs. We describe a tech- nique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. We prove that interval graphs have the same automorphism groups as trees, and for a given interval graph, we construct a tree with the same automorphism group which answers a question of Hanlon [Trans. Amer. Math. Soc 272(2), 1982]. For permutation and circle graphs, we give an inductive characterization by semidirect and wreath prod- ucts. We also prove that every abstract group can be realized by the automorphism group of a comparability graph/poset of the dimension at most four. We also study H-graphs, introduced by Biró, Hujter, and Tuza in 1992. Those are intersection graphs of connected subgraphs of a subdivision of a graph H. This thesis is the first comprehensive...