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In this thesis, we are interested in numerically preserving stationary solutions of balance laws. We start by developing finite volume well-balanced schemes for the system of Euler equations and the system of MHD equations with gravitational source term. Since fluid models and kinetic models are related, this leads us to investigate AP schemes for kinetic equations and their ability to preserve stationary solutions. Kinetic models typically have a stiff term, thus AP schemes are needed to capture good solutions of the model. For such kinetic models, equilibrium solutions are reached after large time. Thus we need a new technique to numerically preserve stationary solutions for AP schemes. We find a criterion for SP schemes for kinetic equations which states, that AP schemes under a particular discretization are also SP. In an attempt to mimic our result for kinetic equations in the context of fluid models, for the isentropic Euler equations we developed an AP scheme in the limit of the Mach number going to zero. Our AP scheme is proven to have a SP property under the condition that the pressure is a function of the density and the latter is obtained as a solution of an elliptic equation. The properties of the schemes we developed and its criteria are validated numerically by various test cases from the literature.
A graph is an abstract network that represents a set of objects, called vertices, and relations between these objects, called edges. Graphs can model various networks. For example, a social network where the vertices correspond to users of the network and the edges represent relations between the users. To better see the structure of a graph it is helpful to visualize it. A standard visualization is a node-link diagram in the Euclidean plane. In such a representation the vertices are drawn as points in the plane and edges are drawn as Jordan curves between every two vertices connected by an edge. Edge crossings decrease the readability of a drawing, therefore, Crossing Optimization is a fundamental problem in Computer Science. This book explores the research frontiers and introduces novel approaches in Crossing Optimization.
This textbook provides an introduction to common methods of performance modeling and analysis of communication systems. These methods form the basis of traffic engineering, teletraffic theory, and analytical system dimensioning. The fundamentals of probability theory, stochastic processes, Markov processes, and embedded Markov chains are presented. Basic queueing models are described with applications in communication networks. Advanced methods are presented that have been frequently used in recent practice, especially discrete-time analysis algorithms, or which go beyond classical performance measures such as Quality of Experience or energy efficiency. Recent examples of modern communication networks include Software Defined Networking and the Internet of Things. Throughout the book, illustrative examples are used to provide practical experience in performance modeling and analysis.
Target group: The book is aimed at students and scientists in computer science and technical computer science, operations research, electrical engineering and economics.
Constraining graph layouts - that is, restricting the placement of vertices and the routing of edges to obey certain constraints - is common practice in graph drawing.
In this book, we discuss algorithmic results on two different restriction types:
placing vertices on the outer face and on the integer grid.
For the first type, we look into the outer k-planar and outer k-quasi-planar graphs, as well as giving a linear-time algorithm to recognize full and closed outer k-planar graphs Monadic Second-order Logic.
For the second type, we consider the problem of transferring a given planar drawing onto the integer grid while perserving the original drawings topology;
we also generalize a variant of Cauchy's rigidity theorem for orthogonal polyhedra of genus 0 to those of arbitrary genus.
Maps are the main tool to represent geographical information. Users often zoom in and out to access maps at different scales. Continuous map generalization tries to make the changes between different scales smooth, which is essential to provide users with comfortable zooming experience.
In order to achieve continuous map generalization with high quality, we optimize some important aspects of maps. In this book, we have used optimization in the generalization of land-cover areas, administrative boundaries, buildings, and coastlines. According to our experiments, continuous map generalization indeed benefits from optimization.
Historical maps are fascinating documents and a valuable source of information for scientists of various disciplines. Many of these maps are available as scanned bitmap images, but in order to make them searchable in useful ways, a structured representation of the contained information is desirable.
This book deals with the extraction of spatial information from historical maps. This cannot be expected to be solved fully automatically (since it involves difficult semantics), but is also too tedious to be done manually at scale.
The methodology used in this book combines the strengths of both computers and humans: it describes efficient algorithms to largely automate information extraction tasks and pairs these algorithms with smart user interactions to handle what is not understood by the algorithm. The effectiveness of this approach is shown for various kinds of spatial documents from the 16th to the early 20th century.
Given points in the plane, connect them using minimum ink. Though the task seems simple, it turns out to be very time consuming. In fact, scientists believe that computers cannot efficiently solve it. So, do we have to resign? This book examines such NP-hard network-design problems, from connectivity problems in graphs to polygonal drawing problems on the plane. First, we observe why it is so hard to optimally solve these problems. Then, we go over to attack them anyway. We develop fast algorithms that find approximate solutions that are very close to the optimal ones. Hence, connecting points with slightly more ink is not hard.
Software frameworks for Realtime Interactive Systems (RIS), e.g., in the areas of Virtual, Augmented, and Mixed Reality (VR, AR, and MR) or computer games, facilitate a multitude of functionalities by coupling diverse software modules. In this context, no uniform methodology for coupling these modules does exist; instead various purpose-built solutions have been proposed. As a consequence, important software qualities, such as maintainability, reusability, and adaptability, are impeded.
Many modern systems provide additional support for the integration of Artificial Intelligence (AI) methods to create so called intelligent virtual environments. These methods exacerbate the above-mentioned problem of coupling software modules in the thus created Intelligent Realtime Interactive Systems (IRIS) even more. This, on the one hand, is due to the commonly applied specialized data structures and asynchronous execution schemes, and the requirement for high consistency regarding content-wise coupled but functionally decoupled forms of data representation on the other.
This work proposes an approach to decoupling software modules in IRIS, which is based on the abstraction of architecture elements using a semantic Knowledge Representation Layer (KRL). The layer facilitates decoupling the required modules, provides a means for ensuring interface compatibility and consistency, and in the end constitutes an interface for symbolic AI methods.
Graphs are a frequently used tool to model relationships among entities. A graph is a binary relation between objects, that is, it consists of a set of objects (vertices) and a set of pairs of objects (edges).
Networks are common examples of modeling data as a graph. For example, relationships between persons in a social network, or network links between computers in a telecommunication network can be represented by a graph.
The clearest way to illustrate the modeled data is to visualize the graphs. The field of Graph Drawing deals with the problem of finding algorithms to automatically generate graph visualizations. The task is to find a "good" drawing, which can be measured by different criteria such as number of crossings between edges or the used area. In this thesis, we study Angular Schematization in Graph Drawing. By this, we mean drawings
with large angles (for example, between the edges at common vertices or at crossing points).
The thesis consists of three parts. First, we deal with the placement of boxes. Boxes are axis-parallel rectangles that can, for example, contain text.
They can be placed on a map to label important sites, or can be used to describe semantic relationships between words in a word network. In the second part of the thesis, we consider graph drawings visually guide the
viewer. These drawings generally induce large angles between edges that meet at a vertex. Furthermore, the edges are drawn crossing-free and in a way that
makes them easy to follow for the human eye. The third and final part is devoted to crossings with large angles. In drawings with crossings, it is important to have large angles between edges at their crossing point, preferably right angles.
Der Einsatz von Multicore-Prozessoren in der industriellen Steuerungstechnik birgt sowohl Chancen als auch Risiken. Die vorliegende Dissertation entwickelt und bewertet aus diesem Grund generische Strategien zur Nutzung dieser Prozessorarchitektur unter Berücksichtigung der spezifischen Rahmenbedingungen und Anforderungen dieser Domäne.
Multicore-Prozessoren bieten die Chance zur Konsolidierung derzeit auf dedizierter Hardware ausgeführter heterogener Steuerungssubsysteme unter einer bisher nicht erreichbaren temporalen Isolation. In diesem Kontext definiert die vorliegende Dissertation die spezifischen Anforderungen, die eine integrierte Ausführung in der Domäne der industriellen Automatisierung erfüllen muss. Eine Vorbedingung für ein derartiges Szenario stellt allerdings der Einsatz einer geeigneten Konsolidierungslösung dar. Mit einem virtualisierten und einem hybriden Konsolidierungsansatz werden deshalb zwei repräsentative Lösungen für die Domäne eingebetteter Systeme vorgestellt, die schließlich hinsichtlich der zuvor definierten Kriterien evaluiert werden.
Da die Taktraten von Prozessoren physikalische Grenzen erreicht haben, werden sich in der Steuerungstechnik signifikante Performanzsteigerungen zukünftig nur durch den Einsatz von Multicore-Prozessoren erzielen lassen. Dies hat zur Vorbedingung, dass die Firmware die Parallelität dieser Prozessorarchitektur in geeigneter Weise zu nutzen vermag. Leider entstehen bei der Parallelisierung eines komplexen Systems wie einer Automatisierungs-Firmware im Allgemeinen signifikante Aufwände. Infolgedessen sollten diesbezügliche Entscheidungen nur auf Basis einer objektiven Abwägung potentieller Alternativen getroffen werden. Allerdings macht die Systemkomplexität eine Abschätzung der durch eine spezifische parallele Firmware-Architektur zu erwartenden Performanz zu einer anspruchsvollen Aufgabe. Dies gilt vor allem, da eine Parallelisierung gefordert wird, die für eine Vielzahl von Lastszenarien in Form gesteuerter Maschinen geeignet ist. Aus diesem Grund spezifiziert die vorliegende Dissertation eine anwendungsorientierte Methode zur Unterstützung von Entwurfsentscheidungen, die bei der Migration einer bestehenden Singlecore-Firmware auf eine homogene Multicore-Architektur zu treffen sind. Dies wird erreicht, indem in automatisierter Weise geeignete Firmware-Modelle auf Basis von dynamischem Profiling der Firmware unter mehreren repräsentativen Lastszenarien erstellt werden. Im Anschluss daran werden diese Modelle um das Expertenwissen von Firmware-Entwicklern erweitert, bevor mittels multikriterieller genetischer Algorithmen der Entwurfsraum der Parallelisierungsalternativen exploriert wird. Schließlich kann eine spezifische Lösung der auf diese Weise hergeleiteten Pareto-Front auf Basis ihrer Bewertungsmetriken zur Implementierung durch einen Entwickler ausgewählt werden. Die vorliegende Arbeit schließt mit einer Fallstudie, welche die zuvor beschriebene Methode auf eine numerische Steuerungs-Firmware anwendet und dabei deren Potential für eine umfassende Unterstützung einer Firmware-Parallelisierung aufzeigt.