Download or read book Query Enumeration and Nowhere Dense Graphs written by Alexandre Vigny and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of my thesis lies between complexity, algorithmic and logic. In particular, we are interested in the complexity of evaluating query.More precisely, given G a finite graph. A query q defines a subset of k-tuples of vertices of G that we note q(G). We call k the arity of q and we then try to efficiently perform the following tasks:1) decide whether the set q G) is empty.2) decide whether a given k-tuplet belongs to the set of solutions q(G).3) calculate the number of solutions.4) enumerate the elements of q(G).Regarding the 4th task, an algorithm that will enumerate the solutions can be decomposed into two steps. The first is called preprocessing and is used to prepare the enumeration. Ideally this step only requires a time linear in the size of the graph. The second step is the enumeration properly speaking. The time needed to get a new solution is called the delay. Ideally we want the delay to not depend on the size of the graph but only on the size of the query. We then talk about constant delay enumeration after linear preprocessing.At the beginning of this thesis, a large part of the interrogations about classes of graphs for which a constant delay enumeration is possible seemed to be located around the classes of nowhere dense graphs.

Download or read book Nowhere Dense Classes of Graphs written by Siebertz, Sebastian and published by Universitätsverlag der TU Berlin. This book was released on 2016-05-24 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: We show that every first-order property of graphs can be decided in almost linear time on every nowhere dense class of graphs. For graph classes closed under taking subgraphs, our result is optimal (under a standard complexity theoretic assumption): it was known before that for all classes C of graphs closed under taking subgraphs, if deciding first-order properties of graphs in C is fixed-parameter tractable, parameterized by the length of the input formula, then C must be nowhere dense. Nowhere dense graph classes form a large variety of classes of sparse graphs including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and graph classes of bounded expansion. For our proof, we provide two new characterisations of nowhere dense classes of graphs. The first characterisation is in terms of a game, which explains the local structure of graphs from nowhere dense classes. The second characterisation is by the existence of sparse neighbourhood covers. On the logical side, we prove a rank-preserving version of Gaifman's locality theorem. The characterisation by neighbourhood covers is based on a characterisation of nowhere dense classes by generalised colouring numbers. We show several new bounds for the generalised colouring numbers on restricted graph classes, such as for proper minor closed classes and for planar graphs. Finally, we study the parameterized complexity of the first-order model-checking problem on structures where an ordering is available to be used in formulas. We show that first-order logic on ordered structures as well as on structures with a successor relation is essentially intractable on nearly all interesting classes. On the other hand, we show that the model-checking problem of order-invariant monadic second-order logic is tractable essentially on the same classes as plain monadic second-order logic and that the model-checking problem for successor-invariant first-order logic is tractable on planar graphs. Wir zeigen, dass jede Eigenschaft von Graphen aus einer nowhere dense Klasse von Graphen, die in der Präadikatenlogik formuliert werden kann, in fast linearer Zeit entschieden werden kann. Dieses Ergebnis ist optimal für Klassen von Graphen, die unter Subgraphen abgeschlossen sind (unter einer Standardannahme aus der Komplexitätstheorie). Um den obigen Satz zu beweisen, führen wir zwei neue Charakterisierungen von nowhere dense Klassen von Graphen ein. Zunächst charakterisieren wir solche Klassen durch ein Spiel, das die lokalen Eigenschaften von Graphen beschreibt. Weiter zeigen wir, dass eine Klasse, die unter Subgraphen abgeschlossen ist, genau dann nowhere dense ist, wenn alle lokalen Nachbarschaften von Graphen der Klasse dünn überdeckt werden können. Weiterhin beweisen wir eine erweiterte Version von Gaifman's Lokalitätssatz für die Prädikatenlogik, der eine Übersetzung von Formeln in lokale Formeln des gleichen Ranges erlaubt. In Kombination erlauben diese neuen Charakterisierungen einen effizienten, rekursiven Lösungsansatz für das Model-Checking Problem der Prädikatenlogik. Die Charakterisierung der nowhere dense Graphklassen durch die oben beschriebenen Überdeckungen basiert auf einer bekannten Charakterisierung durch verallgemeinerte Färbungszahlen. Unser Studium dieser Zahlen führt zu neuen, verbesserten Schranken für die verallgemeinerten Färbungszahlen von nowhere dense Klassen von Graphen, insbesondere für einige wichtige Subklassen, z. B. für Klassen mit ausgeschlossenen Minoren und für planare Graphen. Zuletzt untersuchen wir, welche Auswirkungen eine Erweiterung der Logik durch Ordnungs- bzw. Nachfolgerrelationen auf die Komplexität des Model-Checking Problems hat. Wir zeigen, dass das Problem auf fast allen interessanten Klassen nicht effizient gelöst werden kann, wenn eine beliebige Ordnungs- oder Nachfolgerrelation zum Graphen hinzugefügt wird. Andererseits zeigen wir, dass das Problem für ordnungsinvariante monadische Logik zweiter Stufe auf allen Klassen, für die bekannt ist, dass es für monadische Logik zweiter Stufe effizient gelöst werden kann, auch effizient gelöst werden kann. Wir zeigen, dass das Problem für nachfolgerinvariante Prädikatenlogik auf planaren Graphen effizient gelöst werden kann.

Download or read book SOFSEM 2024 written by Henning Fernau and published by Springer Nature. This book was released on 2024 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 49th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2024, held in Cochem, Germany, in February 2024. The 33 full papers presented in this book were carefully reviewed and selected from 81 submissions. The book also contains one invited talk in full paper length. They focus on original research and challenges in foundations of computer science including algorithms, AI-based methods, computational complexity, and formal models.

Download or read book On Nowhere Dense Graphs written by Jaroslav Nešetřil and published by . This book was released on 2009 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computer Science Theory and Applications written by Edward Hirsch and published by Springer. This book was released on 2014-06-02 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 9th International Computer Science Symposium in Russia, CSR 2014, held in Moscow, Russia, in June 2014. The 27 full papers presented in this volume were carefully reviewed and selected from 76 submissions. In addition the book contains 4 invited lectures. The scope of the proposed topics is quite broad and covers a wide range of areas in theoretical computer science and its applications.

Download or read book Sparsity written by Jaroslav Nešetřil and published by Springer Science & Business Media. This book was released on 2012-04-24 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.

Download or read book Nowhere Dense Classes of Graphs written by Sebastian Siebertz and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Classical Descriptive Set Theory written by Alexander Kechris and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.

Download or read book Data Intensive Text Processing with MapReduce written by Jimmy Lin and published by Springer Nature. This book was released on 2022-05-31 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our world is being revolutionized by data-driven methods: access to large amounts of data has generated new insights and opened exciting new opportunities in commerce, science, and computing applications. Processing the enormous quantities of data necessary for these advances requires large clusters, making distributed computing paradigms more crucial than ever. MapReduce is a programming model for expressing distributed computations on massive datasets and an execution framework for large-scale data processing on clusters of commodity servers. The programming model provides an easy-to-understand abstraction for designing scalable algorithms, while the execution framework transparently handles many system-level details, ranging from scheduling to synchronization to fault tolerance. This book focuses on MapReduce algorithm design, with an emphasis on text processing algorithms common in natural language processing, information retrieval, and machine learning. We introduce the notion of MapReduce design patterns, which represent general reusable solutions to commonly occurring problems across a variety of problem domains. This book not only intends to help the reader "think in MapReduce", but also discusses limitations of the programming model as well. Table of Contents: Introduction / MapReduce Basics / MapReduce Algorithm Design / Inverted Indexing for Text Retrieval / Graph Algorithms / EM Algorithms for Text Processing / Closing Remarks

Download or read book Art Gallery Theorems and Algorithms written by Joseph O'Rourke and published by Oxford University Press, USA. This book was released on 1987 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry.

Download or read book Foundations of Data Science written by Avrim Blum and published by Cambridge University Press. This book was released on 2020-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Download or read book The Algorithm Design Manual written by Steven S Skiena and published by Springer Science & Business Media. This book was released on 2009-04-05 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography. NEW to the second edition: • Doubles the tutorial material and exercises over the first edition • Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video • Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them • Includes several NEW "war stories" relating experiences from real-world applications • Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java

Download or read book Sophie s World written by Jostein Gaarder and published by Farrar, Straus and Giroux. This book was released on 2007-03-20 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: A page-turning novel that is also an exploration of the great philosophical concepts of Western thought, Jostein Gaarder's Sophie's World has fired the imagination of readers all over the world, with more than twenty million copies in print. One day fourteen-year-old Sophie Amundsen comes home from school to find in her mailbox two notes, with one question on each: "Who are you?" and "Where does the world come from?" From that irresistible beginning, Sophie becomes obsessed with questions that take her far beyond what she knows of her Norwegian village. Through those letters, she enrolls in a kind of correspondence course, covering Socrates to Sartre, with a mysterious philosopher, while receiving letters addressed to another girl. Who is Hilde? And why does her mail keep turning up? To unravel this riddle, Sophie must use the philosophy she is learning—but the truth turns out to be far more complicated than she could have imagined.

Download or read book A Course in Combinatorics written by J. H. van Lint and published by Cambridge University Press. This book was released on 2001-11-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Download or read book Computable Structure Theory written by Antonio Montalbán and published by Cambridge University Press. This book was released on 2021-06-24 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematics, we know there are some concepts - objects, constructions, structures, proofs - that are more complex and difficult to describe than others. Computable structure theory quantifies and studies the complexity of mathematical structures, structures such as graphs, groups, and orderings. Written by a contemporary expert in the subject, this is the first full monograph on computable structure theory in 20 years. Aimed at graduate students and researchers in mathematical logic, it brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework, making it easier for the reader to learn the main results and techniques in the area for application in their own research. This volume focuses on countable structures whose complexity can be measured within arithmetic; a forthcoming second volume will study structures beyond arithmetic.

Download or read book Measure Integral and Probability written by Marek Capinski and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

Download or read book Persistence Theory From Quiver Representations to Data Analysis written by Steve Y. Oudot and published by American Mathematical Soc.. This book was released on 2017-05-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.