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We consider competitive location problems where two competing providers place their facilities sequentially and users can decide between the competitors. We assume that both competitors act non-cooperatively and aim at maximizing their own benefits. We investigate the complexity and approximability of such problems on graphs, in particular on simple graph classes such as trees and paths. We also develop fast algorithms for single competitive location problems where each provider places a single facilty. Voting location, in contrast, aims at identifying locations that meet social criteria. The provider wants to satisfy the users (customers) of the facility to be opened. In general, there is no location that is favored by all users. Therefore, a satisfactory compromise has to be found. To this end, criteria arising from voting theory are considered. The solution of the location problem is understood as the winner of a virtual election among the users of the facilities, in which the potential locations play the role of the candidates and the users represent the voters. Competitive and voting location problems turn out to be closely related.
Complexity and Partitions
(2001)
Computational complexity theory usually investigates the complexity of sets, i.e., the complexity of partitions into two parts. But often it is more appropriate to represent natural problems by partitions into more than two parts. A particularly interesting class of such problems consists of classification problems for relations. For instance, a binary relation R typically defines a partitioning of the set of all pairs (x,y) into four parts, classifiable according to the cases where R(x,y) and R(y,x) hold, only R(x,y) or only R(y,x) holds or even neither R(x,y) nor R(y,x) is true. By means of concrete classification problems such as Graph Embedding or Entailment (for propositional logic), this thesis systematically develops tools, in shape of the boolean hierarchy of NP-partitions and its refinements, for the qualitative analysis of the complexity of partitions generated by NP-relations. The Boolean hierarchy of NP-partitions is introduced as a generalization of the well-known and well-studied Boolean hierarchy (of sets) over NP. Whereas the latter hierarchy has a very simple structure, the situation is much more complicated for the case of partitions into at least three parts. To get an idea of this hierarchy, alternative descriptions of the partition classes are given in terms of finite, labeled lattices. Based on these characterizations the Embedding Conjecture is established providing the complete information on the structure of the hierarchy. This conjecture is supported by several results. A natural extension of the Boolean hierarchy of NP-partitions emerges from the lattice-characterization of its classes by considering partition classes generated by finite, labeled posets. It turns out that all significant ideas translate from the case of lattices. The induced refined Boolean hierarchy of NP-partitions enables us more accuratly capturing the complexity of certain relations (such as Graph Embedding) and a description of projectively closed partition classes.
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.
In many cases, problems, data, or information can be modeled as graphs. Graphs can be used as a tool for modeling in any case where connections between distinguishable objects occur. Any graph consists of a set of objects, called vertices, and a set of connections, called edges, such that any edge connects a pair of vertices. For example, a social network can be modeled by a graph by
transforming the users of the network into vertices and friendship relations between users into edges. Also physical networks like computer networks or transportation networks, for example, the metro network of a city, can be seen as graphs.
For making graphs and, thereby, the data that is modeled, well-understandable for users, we need a visualization. Graph drawing deals with algorithms for visualizing graphs. In this thesis, especially the use of crossings and curves is investigated for graph drawing problems under additional constraints. The constraints that occur in the problems investigated in this thesis especially restrict the positions of (a part of) the vertices; this is done either as a hard constraint or as an optimization criterion.
The landscape of today’s programming languages is manifold. With the diversity of applications, the difficulty of adequately addressing and specifying the used programs increases. This often leads to newly designed and implemented domain-specific languages. They enable domain experts to express knowledge in their preferred format, resulting in more readable and concise programs. Due to its flexible and declarative syntax without reserved keywords, the logic programming language Prolog is particularly suitable for defining and embedding domain-specific languages.
This thesis addresses the questions and challenges that arise when integrating domain-specific languages into Prolog. We compare the two approaches to define them either externally or internally, and provide assisting tools for each. The grammar of a formal language is usually defined in the extended Backus–Naur form. In this work, we handle this formalism as a domain-specific language in Prolog, and define term expansions that allow to translate it into equivalent definite clause grammars. We present the package library(dcg4pt) for SWI-Prolog, which enriches them by an additional argument to automatically process the term’s corresponding parse tree. To simplify the work with definite clause grammars, we visualise their application by a web-based tracer.
The external integration of domain-specific languages requires the programmer to keep the grammar, parser, and interpreter in sync. In many cases, domain-specific languages can instead be directly embedded into Prolog by providing appropriate operator definitions. In addition, we propose syntactic extensions for Prolog to expand its expressiveness, for instance to state logic formulas with their connectives verbatim. This allows to use all tools that were originally written for Prolog, for instance code linters and editors with syntax highlighting. We present the package library(plammar), a standard-compliant parser for Prolog source code, written in Prolog. It is able to automatically infer from example sentences the required operator definitions with their classes and precedences as well as the required Prolog language extensions. As a result, we can automatically answer the question: Is it possible to model these example sentences as valid Prolog clauses, and how?
We discuss and apply the two approaches to internal and external integrations for several domain-specific languages, namely the extended Backus–Naur form, GraphQL, XPath, and a controlled natural language to represent expert rules in if-then form. The created toolchain with library(dcg4pt) and library(plammar) yields new application opportunities for static Prolog source code analysis, which we also present.
Today’s Internet architecture was not designed from scratch but was driven by new services that emerged during its development. Hence, it is often described as patchwork where additional patches are applied in case new services require modifications to the existing architecture. This process however is rather slow and hinders the development of innovative network services with certain architecture or network requirements. Currently discussed technologies like Software-Defined Networking (SDN) or Network Virtualization (NV) are seen as key enabling technologies to overcome this rigid best effort legacy of the Internet. Both technologies offer the possibility to create virtual networks that accommodate the specific needs of certain services. These logical networks are operated on top of a physical substrate and facilitate flexible network resource allocation as physical resources can be added and removed depending on the current network and load situation. In addition, the clear separation and isolation of networks foster the development of application-aware networks that fulfill the special requirements of emerging applications. A prominent use case that benefits from these extended capabilities of the network is denoted with service component mobility. Services hosted on Virtual Machines (VMs) follow their consuming mobile endpoints, so that access latency as well as consumed network resources are reduced. Especially for applications like video streaming, which consume a large fraction of the available resources, is this an important means to relieve the resource constraints and eventually provide better service quality. Service and endpoint mobility both allow an adaptation of the used paths between an offered service, i.e., video streaming and the consuming users in case the service quality drops due to network problems. To make evidence-based adaptations in case of quality drops, a scalable monitoring component is required that is able to monitor the service quality for video streaming applications with reliable accuracy. This monograph details challenges that arise when deploying a certain service, i.e., video streaming, in a future virtualized network architecture and discusses possible solutions. In particular, this work evaluates the performance of mechanisms enabling service mobility and presents an optimized architecture for service mobility. Concerning endpoint mobility, improvements are developed that reduce the latency between endpoints and consumed services and ensure connectivity regardless of the used mobile access network. In the last part, a network-based video quality monitoring solution is developed and its accuracy is evaluated.
Das stochastische Denken, die Bernoullische Stochastik und dessen informationstechnologische Umsetzung, namens Stochastikon stellen die Grundlage für das Verständnis und die erfolgreiche Nutzung einer stochastischen Wissenschaft dar. Im Rahmen dieser Arbeit erfolgt eine Klärung des Begriffs des stochastischen Denkens, eine anschauliche Darstellung der von Elart von Collani entwickelten Bernoullischen Stochastik und eine Beschreibung von Stochastikon. Dabei werden sowohl das Gesamtkonzept von Stochastikon, sowie die Ziele, Aufgaben und die Realisierung der beiden Teilsysteme namens Mentor und Encyclopedia vorgestellt. Das stochastische Denken erlaubt eine realitätsnahe Sichtweise der Dinge, d.h. eine Sichtweise, die mit den menschlichen Beobachtungen und Erfahrungen im Einklang steht und somit die Unsicherheit über zukünftige Entwicklungen berücksichtigt. Der in diesem Kontext verwendete Begriff der Unsicherheit bezieht sich ausschließlich auf zukünftige Entwicklungen und äußert sich in Variabilität. Quellen der Unsicherheit sind einerseits die menschliche Ignoranz und andererseits der Zufall. Unter Ignoranz wird hierbei die Unwissenheit des Menschen über die unbekannten, aber feststehenden Fakten verstanden, die die Anfangsbedingungen der zukünftigen Entwicklung repräsentieren. Die Bernoullische Stochastik liefert ein Regelwerk und ermöglicht die Entwicklung eines quantitativen Modells zur Beschreibung der Unsicherheit und expliziter Einbeziehung der beiden Quellen Ignoranz und Zufall. Das Modell trägt den Namen Bernoulli-Raum und bildet die Grundlage für die Herleitung quantitativer Verfahren, um zuverlässige und genaue Aussagen sowohl über die nicht-existente zufällige Zukunft (Vorhersageverfahren), als auch über die unbekannte feststehende Vergangenheit (Messverfahren). Das Softwaresystem Stochastikon implementiert die Bernoullische Stochastik in Form einer Reihe autarker, miteinander kommunizierender Teilsysteme. Ziel des Teilsystems Encyclopedia ist die Bereitstellung und Bewertung stochastischen Wissens. Das Teilsystem Mentor dient der Unterstützung des Anwenders bei der Problemlösungsfindung durch Identifikation eines richtigen Modells bzw. eines korrekten Bernoulli-Raums. Der Lösungsfindungsprozess selber enthält keinerlei Unsicherheit. Die ganze Unsicherheit steckt in der Lösung, d.h. im Bernoulli-Raum, der explizit die vorhandene Unwissenheit (Ignoranz) und den vorliegenden Zufall abdeckend enthält.
3D point clouds are a de facto standard for 3D documentation and modelling. The advances in laser scanning technology broadens the usability and access to 3D measurement systems. 3D point clouds are used in many disciplines such as robotics, 3D modelling, archeology and surveying. Scanners are able to acquire up to a million of points per second to represent the environment with a dense point cloud. This represents the captured environment with a very high degree of detail. The combination of laser scanning technology with photography adds color information to the point clouds. Thus the environment is represented more realistically. Full 3D models of environments, without any occlusion, require multiple scans. Merging point clouds is a challenging process. This thesis presents methods for point cloud registration based on the panorama images generated from the scans. Image representation of point clouds introduces 2D image processing methods to 3D point clouds. Several projection methods for the generation of panorama maps of point clouds are presented in this thesis. Additionally, methods for point cloud reduction and compression based on the panorama maps are proposed. Due to the large amounts of data generated from the 3D measurement systems these methods are necessary to improve the point cloud processing, transmission and archiving. This thesis introduces point cloud processing methods as a novel framework for the digitisation of archeological excavations. The framework replaces the conventional documentation methods for excavation sites. It employs point clouds for the generation of the digital documentation of an excavation with the help of an archeologist on-site. The 3D point cloud is used not only for data representation but also for analysis and knowledge generation. Finally, this thesis presents an autonomous indoor mobile mapping system. The mapping system focuses on the sensor placement planning method. Capturing a complete environment requires several scans. The sensor placement planning method solves for the minimum required scans to digitise large environments. Combining this method with a navigation system on a mobile robot platform enables it to acquire data fully autonomously. This thesis introduces a novel hole detection method for point clouds to detect obscured parts of a captured environment. The sensor placement planning method selects the next scan position with the most coverage of the obscured environment. This reduces the required number of scans. The navigation system on the robot platform consist of path planning, path following and obstacle avoidance. This guarantees the safe navigation of the mobile robot platform between the scan positions. The sensor placement planning method is designed as a stand alone process that could be used with a mobile robot platform for autonomous mapping of an environment or as an assistant tool for the surveyor on scanning projects.
In der Arbeit wird ein neues Konzept für Fahrsimulator-Datenbasen vorgestellt. Der Anwender entwirft eine auf seine Fragestellung zugeschnittene Datenbasis mithilfe einer einfachen Skriptsprache. Das Straßennetzwerk wird auf einer topologischen Ebene repäsentiert. In jedem Simulationsschritt wird hieraus im Sichtbarkeitsbereich des Fahrers die geometrische Repäsentation berechnet. Die für den Fahrer unsichtbaren Teile des Straßenetzwerks können während der Simulation verändert werden. Diese Veränderungen können von der Route des Fahrers oder von den in der Simulation erhobenen Messerten abhängen. Zudem kann der Anwender das Straßennetzwerk interaktiv verändern. Das vorgestellte Konzept bietet zahlreiche Möglichkeiten zur Erzeugung reproduzierbarer Szenarien für Experimente in Fahrsimulatoren.
This work is subdivided into two main areas: resilient admission control and resilient routing. The work gives an overview of the state of the art of quality of service mechanisms in communication networks and proposes a categorization of admission control (AC) methods. These approaches are investigated regarding performance, more precisely, regarding the potential resource utilization by dimensioning the capacity for a network with a given topology, traffic matrix, and a required flow blocking probability. In case of a failure, the affected traffic is rerouted over backup paths which increases the traffic rate on the respective links. To guarantee the effectiveness of admission control also in failure scenarios, the increased traffic rate must be taken into account for capacity dimensioning and leads to resilient AC. Capacity dimensioning is not feasible for existing networks with already given link capacities. For the application of resilient NAC in this case, the size of distributed AC budgets must be adapted according to the traffic matrix in such a way that the maximum blocking probability for all flows is minimized and that the capacity of all links is not exceeded by the admissible traffic rate in any failure scenario. Several algorithms for the solution of that problem are presented and compared regarding their efficiency and fairness. A prototype for resilient AC was implemented in the laboratories of Siemens AG in Munich within the scope of the project KING. Resilience requires additional capacity on the backup paths for failure scenarios. The amount of this backup capacity depends on the routing and can be minimized by routing optimization. New protection switching mechanisms are presented that deviate the traffic quickly around outage locations. They are simple and can be implemented, e.g, by MPLS technology. The Self-Protecting Multi-Path (SPM) is a multi-path consisting of disjoint partial paths. The traffic is distributed over all faultless partial paths according to an optimized load balancing function both in the working case and in failure scenarios. Performance studies show that the network topology and the traffic matrix also influence the amount of required backup capacity significantly. The example of the COST-239 network illustrates that conventional shortest path routing may need 50% more capacity than the optimized SPM if all single link and node failures are protected.