## 004 Datenverarbeitung; Informatik

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Practical optimization problems often comprise several incomparable and conflicting objectives. When booking a trip using several means of transport, for instance, it should be fast and at the same time not too expensive. The first part of this thesis is concerned with the algorithmic solvability of such multiobjective optimization problems. Several solution notions are discussed and compared with respect to their difficulty. Interestingly, these solution notions are always equally difficulty for a single-objective problem and they differ considerably already for two objectives (unless P = NP). In this context, the difference between search and decision problems is also investigated in general. Furthermore, new and improved approximation algorithms for several variants of the traveling salesperson problem are presented. Using tools from discrepancy theory, a general technique is developed that helps to avoid an obstacle that is often hindering in multiobjective approximation: The problem of combining two solutions such that the new solution is balanced in all objectives and also mostly retains the structure of the original solutions. The second part of this thesis is dedicated to several aspects of systems of equations for (formal) languages. Firstly, conjunctive and Boolean grammars are studied, which are extensions of context-free grammars by explicit intersection and complementation operations, respectively. Among other results, it is shown that one can considerably restrict the union operation on conjunctive grammars without changing the generated language. Secondly, certain circuits are investigated whose gates do not compute Boolean values but sets of natural numbers. For these circuits, the equivalence problem is studied, i.\,e.\ the problem of deciding whether two given circuits compute the same set or not. It is shown that, depending on the allowed types of gates, this problem is complete for several different complexity classes and can thus be seen as a parametrized) representative for all those classes.

Der große Vorteil eines q-Gramm Indexes liegt darin, dass es möglich ist beliebige Zeichenketten in einer Dokumentensammlung zu suchen. Ein Nachteil jedoch liegt darin, dass bei größer werdenden Datenmengen dieser Index dazu neigt, sehr groß zu werden, was mit einem deutlichem Leistungsabfall verbunden ist. In dieser Arbeit wird eine neuartige Technik vorgestellt, die die Leistung eines q-Gramm Indexes mithilfe zusätzlicher M-Matrizen für jedes q-Gramm und durch die Kombination mit einem invertierten Index erhöht. Eine M-Matrix ist eine Bit-Matrix, die Informationen über die Positionen eines q-Gramms enthält. Auch bei der Kombination von zwei oder mehreren Q-Grammen bieten diese M-Matrizen Informationen über die Positionen der Kombination. Dies kann verwendet werden, um die Komplexität der Zusammenführung der q-Gramm Trefferlisten für eine gegebene Suchanfrage zu reduzieren und verbessert die Leistung des n-Gramm-invertierten Index. Die Kombination mit einem termbasierten invertierten Index beschleunigt die durchschnittliche Suchzeit zusätzlich und vereint die Vorteile beider Index-Formate. Redundante Informationen werden in dem q-Gramm Index reduziert und weitere Funktionalität hinzugefügt, wie z.B. die Bewertung von Treffern nach Relevanz, die Möglichkeit, nach Konzepten zu suchen oder Indexpartitionierungen nach Wichtigkeit der enthaltenen Terme zu erstellen.

In the future Internet, the people-centric communication paradigm will be complemented by a ubiquitous communication among people and devices, or even a communication between devices. This comes along with the need for a more flexible, cheap, widely available Internet access. Two types of wireless networks are considered most appropriate for attaining those goals. While wireless sensor networks (WSNs) enhance the Internet’s reach by providing data about the properties of the environment, wireless mesh networks (WMNs) extend the Internet access possibilities beyond the wired backbone. This monograph contains four chapters which present modeling and optimization methods for WSNs and WMNs. Minimizing energy consumptions is the most important goal of WSN optimization and the literature consequently provides countless energy consumption models. The first part of the monograph studies to what extent the used energy consumption model influences the outcome of analytical WSN optimizations. These considerations enable the second contribution, namely overcoming the problems on the way to a standardized energy-efficient WSN communication stack based on IEEE 802.15.4 and ZigBee. For WMNs both problems are of minor interest whereas the network performance has a higher weight. The third part of the work, therefore, presents algorithms for calculating the max-min fair network throughput in WMNs with multiple link rates and Internet gateway. The last contribution of the monograph investigates the impact of the LRA concept which proposes to systematically assign more robust link rates than actually necessary, thereby allowing to exploit the trade-off between spatial reuse and per-link throughput. A systematical study shows that a network-wide slightly more conservative LRA than necessary increases the throughput of a WMN where max-min fairness is guaranteed. It moreover turns out that LRA is suitable for increasing the performance of a contention-based WMN and is a valuable optimization tool.

Currently, we observe a strong growth of services and applications, which use the Internet for data transport. However, the network requirements of these applications differ significantly. This makes network management difficult, since it complicated to separate network flows into application classes without inspecting application layer data. Network virtualization is a promising solution to this problem. It enables running different virtual network on the same physical substrate. Separating networks based on the service supported within allows controlling each network according to the specific needs of the application. The aim of such a network control is to optimize the user perceived quality as well as the cost efficiency of the data transport. Furthermore, network virtualization abstracts the network functionality from the underlying implementation and facilitates the split of the currently tightly integrated roles of Internet Service Provider and network owner. Additionally, network virtualization guarantees that different virtual networks run on the same physical substrate do not interfere with each other. This thesis discusses different aspects of the network virtualization topic. It is focused on how to manage and control a virtual network to guarantee the best Quality of Experience for the user. Therefore, a top-down approach is chosen. Starting with use cases of virtual networks, a possible architecture is derived and current implementation options based on hardware virtualization are explored. In the following, this thesis focuses on assessing the Quality of Experience perceived by the user and how it can be optimized on application layer. Furthermore, options for measuring and monitoring significant network parameters of virtual networks are considered.

The field of small satellite formations and constellations attracted growing attention, based on recent advances in small satellite engineering. The utilization of distributed space systems allows the realization of innovative applications and will enable improved temporal and spatial resolution in observation scenarios. On the other side, this new paradigm imposes a variety of research challenges. In this monograph new networking concepts for space missions are presented, using networks of ground stations. The developed approaches combine ground station resources in a coordinated way to achieve more robust and efficient communication links. Within this thesis, the following topics were elaborated to improve the performance in distributed space missions: Appropriate scheduling of contact windows in a distributed ground system is a necessary process to avoid low utilization of ground stations. The theoretical basis for the novel concept of redundant scheduling was elaborated in detail. Additionally to the presented algorithm was a scheduling system implemented, its performance was tested extensively with real world scheduling problems. In the scope of data management, a system was developed which autonomously synchronizes data frames in ground station networks and uses this information to detect and correct transmission errors. The system was validated with hardware in the loop experiments, demonstrating the benefits of the developed approach.