Library

Description: Im Mai 2009 wurde Wolfram|Alpha gestartet, ein Service, der seinen Namen von seinem Entwickler, dem britischen Mathematiker Stephen Wolfram, ableitet. Dem Benutzer soll nicht nur eine Liste von Webseiten als Ergebnis auf Anfragen geliefert werden, sondern Antworten auf konkrete Fragen geben. In diesem Report soll gezeigt werden, warum sichWolframjAlpha von Suchmaschinen abgrenzt und was die Berechnung von Antworten auf natürlichsprachliche Fragen möglich machen kann.

Description: Wolfram|Alpha was started in May 2009 and it's a service whose name derives from the british mathematician Stephen wolfram. As a result for a request the user is not just supported with a list of websites but with answers for concrete questions. In this report it will be shown why Wolfram|Alpha seperates from search engines and moreover what makes the computation of answers for natural language queries possible.

Description: We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.

Description: Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term “multiply structured exterior domain” is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.

Description: We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph.

Description: Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity-flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of MIPs coming from network design problems by a factor of two on average.

Description: Executing applications in the Grid often requires access to multiple geographically distributed resources. In a Grid environment, these resources belong to different administrative domains, each employing its own scheduling policy. That is, at which time an activity (e.g., compute job, data transfer) is started, is decided by the resource's local management system. In such an environment, the coordinated execution of distributed applications requires guarantees on the quality of service (QoS) of the needed resources. Reserving resources in advance is an accepted means to obtain QoS guarantees from a single provider. The challenge, however, is to coordinate advance reservations of multiple resources. This work presents a system architecture and mechanisms to coordinate multiple advance reservations -- called co-reservations -- for delivering QoS guarantees to complex applications. We formally define the co-reservation problem as an optimization problem. The presented model supports three dimensions of freedom: the start time, the duration and the service level of a reservation. Requests and resources are described in a simple language. After matching the static properties and requirements of either side in a mapping, the reservation mechanism probes information about the future status of the resources. The versatile design of the probing step allows the efficient processing of requests, but also lets the resources express their preferences among the myriads of reservation candidates. Next, the best mapping is found through an implementation of the formal co-reservation model. Then, the mapping has to be secured, i.e., resources need to be allocated to a co-reservation candidate with all-or-nothing semantics. We study several goal-driven sequential and concurrent allocation mechanisms and define schemes for handling allocation failures. Finally, we introduce the concept of virtual resources for seamlessly embedding co-reservations into Grid resource management.

Description: Die Ausführung von Anwendungen erfordert oft mehrere, geographisch verteilte Ressourcen. In Grid-Umgebungen gehören diese Ressourcen zu verschiedenen administrativen Organisationen, wobei jede ihre eigene Schedulingregeln verwendet. Das bedeutet, zu welcher Zeit eine Aktivität gestartet wird (z.B. ein Rechenjob), wird vom lokalen Ressourcenmanagementsystem entschieden. Die koordinierte Ausführung von verteilten Anwendungen erfordert Dienstgütegarantien für die benötigten Ressourcen. Das Reservieren von Ressourcen im Voraus ist ein Mittel, um Dienstgütegarantien von einem einzelnen Ressourcenanbieter zu erhalten. Die Herausforderung in dieser Arbeit ist, Vorausreservierungen von mehreren Ressourcen zu koordinieren. Es wird ein System für die Koordinierung mehrerer Vorausreservierungen -- Co-Reservierungen genannt -- für die Bereitstellung von Dienstgütegarantien vorgestellt. Wir definieren das Co-Reservierungsproblem als Optimierungsproblem. Das vorgestellte Modell unterstützt drei Freiheitsgrade: die Startzeit, die Dauer und die Dienstgüte einer Reservierung. Anfragen und Ressourcen werden in einer einfachen Sprache beschrieben. Nachdem statische Eigenschaften und Anforderungen beider Seiten überprüft wurden, ermittelt der Reservierungsmechanismus Informationen über den zukünftigen Zustand der Ressourcen. Dieser Schritt ist so allgemein gehalten, daß er sowohl ein effizientes Bearbeiten der Anfragen erlaubt als auch den Ressourcen ermöglicht ihre Präferenzen auszudrücken. Im Anschluss wird die optimale Zuweisung von Anfragen zu Ressourcen ermittelt. Im letzten Schritt muss diese Zuweisung umgesetzt werden, d.h., entweder alle oder keine Ressource wird allokiert. Es werden mehrere sequentielle und parallele Allokationsverfahren vorgestellt sowie deren Auswirkung auf verschiedene Metriken untersucht. Die Einbettung von Co-Reservierungen in das Grid-Ressourcenmanagement wird anhand des Konzeptes der virtuellen Ressource dargestellt.

Description: Vorbemerkung Beim Schreiben dieses Artikels, der auf Veränderungen der Kommunikations- und Publikationstechniken und ihre Bedeutung hinweist, ist uns mehr als je zuvor bewusst geworden, wie beschränkt das Medium Papier ist. Es gibt z. B. keine Hyperlinks, durch die man unmittelbar das Erwähnte erleben oder überprüfen kann. Ein schneller Wechsel vom Wort zum Bild, zum Ton oder Video ist nicht möglich. Wer will schon lange URLs abtippen und Medienbrüche erleiden? Wir haben uns daher entschlossen, eine textidentische Version dieses Artikels mit allen URLs – sie liegt Ihnen hier vor – elektronisch anzubieten und in der für die "Gegenworte" (BBAW) gekürzten Fassung nur durch [URL] anzudeuten, dass der Leser an dieser Stelle einfach in der elektronischen Version einen Klick ins Internet machen sollte. Und damit sind wir bereits mitten im Thema.

Description: Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.

Description: The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem, namely, the Steiner cut and the Steiner partition inequalities, as well as the associated polynomial time separation algorithms, can be generalized. Similar to the Steiner tree case, a directed formulation, which is stronger than the natural undirected one, plays a central role.

Description: Zwischen dem Bibliotheksverbund Bayern (BVB) und dem Kooperativen Bibliotheksverbund Berlin-Brandenburg (KOBV) besteht seit Ende 2007 eine Strategische Allianz, die auf zwei Säulen beruht: einer langfristigen Entwicklungspartnerschaft einerseits und der Kooperation im Dienstleistungsbereich mit der Integration der Verbundkataloge andererseits. Ende 2008 wurde das erste Entwicklungsprojekt "Literaturverwaltungsprogramme" abgeschlossen, dessen Ergebnisse in dieser Handreichung in Form von Handlungsempfehlungen für Bibliotheken vorgestellt werden. Ziel des Projekts war es, den Datenaustausch zwischen den Bibliotheks- und Verbundkatalogen des BVB und KOBV und gängigen Literaturverwaltungsprogrammen zu optimieren. Neben Handlungsempfehlungen für die Implementierung neuer Exportschnittstellen und die Verbesserung bestehender Exportmöglichkeiten werden Hinweise auf verbesserte Nutzerführung gegeben. Die Empfehlungen beziehen sich vorwiegend auf den Datenaustausch zwischen den Bibliothekssystemen Aleph 500, MetaLib und WebOPAC/InfoGuide und den Literaturverwaltungsprogrammen Citavi, EndNote, RefWorks und Zotero.

Description: Every day, millions of people are transported by buses, trains, and airplanes in Germany. Public transit (PT) is of major importance for the quality of life of individuals as well as the productivity of entire regions. Quality and efficiency of PT systems depend on the political framework (state-run, market oriented) and the suitability of the infrastructure (railway tracks, airport locations), the existing level of service (timetable, flight schedule), the use of adequate technologies (information, control, and booking systems), and the best possible deployment of equipment and resources (energy, vehicles, crews). The decision, planning, and optimization problems arising in this context are often gigantic and “scream” for mathematical support because of their complexity. This article sketches the state and the relevance of mathematics in planning and operating public transit, describes today’s challenges, and suggests a number of innovative actions. The current contribution of mathematics to public transit is — depending on the transportation mode — of varying depth. Air traffic is already well supported by mathematics. Bus traffic made significant advances in recent years, while rail traffic still bears significant opportunities for improvements. In all areas of public transit, the existing potentials are far from being exhausted. For some PT problems, such as vehicle and crew scheduling in bus and air traffic, excellent mathematical tools are not only available, but used in many places. In other areas, such as rolling stock rostering in rail traffic, the performance of the existing mathematical algorithms is not yet sufficient. Some topics are essentially untouched from a mathematical point of view; e.g., there are (except for air traffic) no network design or fare planning models of practical relevance. PT infrastructure construction is essentially devoid of mathematics, even though enormous capital investments are made in this area. These problems lead to questions that can only be tackled by engineers, economists, politicians, and mathematicians in a joint effort. Among other things, the authors propose to investigate two specific topics, which can be addressed at short notice, are of fundamental importance not only for the area of traffic planning, should lead to a significant improvement in the collaboration of all involved parties, and, if successful, will be of real value for companies and customers: • discrete optimal control: real-time re-planning of traffic systems in case of disruptions, • model integration: service design in bus and rail traffic. Work on these topics in interdisciplinary research projects could be funded by the German ministry of research and education (BMBF), the German ministry of economics (BMWi), or the German science foundation (DFG).

Description: The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.

Description: Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing paths forms a valid routing and, if this is not the case, to find a small subset of the given paths that cannot be shortest paths simultaneously for any routing lengths. In this paper we show that it is NP-hard to approximate the size of the smallest shortest path conflict by a factor less than 7/6.

Description: The Vehicle Positioning Problem (VPP) consists of the assignment of vehicles (buses, trams or trains) of a public transport or railway company to parking positions in a depot and to timetabled trips. Such companies have many different types of vehicles, and each trip can be performed only by vehicles of some of these types. These assignments are non-trivial due to the topology of depots. The parking positions are organized in tracks, which work as one- or two-sided stacks or queues. If a required type of vehicle is not available in the front of any track, shunting movements must be performed in order to change vehicles' positions, which is undesirable and should be avoided. In this text we present integer linear and non-linear programming formulations for some versions of the problem and compare them from a theoretical and a computational point of view.

Description: The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.

Description: Das Verständnis von geometrischen Strukturen und dynamischen Eigenschaften molekularer Konformationen ist essentiell für die Vorhersage des Langzeitverhaltens von Molekülen. Die Identifikation metastabiler Konformationen sowie die Bestimmung von Übergangswahrscheinlichkeiten und Haltezeiten sind Bestandteil der Konformationdynamik. Dabei handelt es sich um eine Mehrskalenmethode, die auf eine reduzierte Beschreibung des Systems mittels einer stochastischen Übergangsmatrix führt. In der vorliegenden Dissertation wurde untersucht, wie man die Genauigkeit der Matrizen sowie der daraus berechneten Größen quantifizieren kann. Im Mittelpunkt stehen dabei Fehlerschätzer für den invarianten Unterraum, da die rechten Eigenvektoren als Grundlage der Robusten Perron Cluster Analyse (PCCA+) zur Identifizierung der metastabilen Konformationen dienen. Die Zerlegung des Zustandsraumes in Basisfunktionen sowie die Approximation der Matrixeinträge mittels Monte-Carlo-Quadratur führen zu zeilenweise korrelierten Zufallsmatrizen. Mit Hilfe einer stochastischen Norm sowie einem geeigneten statistischen Modell für die Verteilung der Matrixzeilen können u.a. Fehlerschranken und -verteilungen für den invarianten Unterraum brechnet werden. Eine Equilibrierung des Fehlers zwischen den Basisfunktionen kann durch erweitertes Sampling in solchen Regionen erreicht werden, in denen die Trajektorien nur langsam mischen.Eine hierarchische Zerlegung dieser Basisfunktionen verbessert systematisch die Zerlegung in metastabile Konformationen, indem sie den Fehler im invarianten Unterraum reduziert. Diese Techniken gestatten eine Evaluierung der Simulationsergebnisse und ebnen den Weg zur Behandlung komplexerer Moleküle. Desweiteren wurden Verallgemeinerungen der PCCA+ untersucht. Die Erweiterung der PCCA+ auf nicht-reversible Markov-Ketten sowie die Modifizierung der Zielfunktion für den Fall der weichen Clusterung setzen die Entwicklung von der PCCA über PCCA+ zu PCCA++ fort. Somit können neue Anwendungsfelder für dieses Cluster-Verfahren erschlossen werden. Die Methoden wurden zwar in Rahmen der Konformationsdynamik entwickelt, jedoch lassen sie sich auf eine weite Problemklasse anwenden, in der Gebietszerlegungsverfahren mit Monte-Carlo-Quadratur kombiniert werden. Mögliche Anwendungsgebiete umfassen die chemische Master-Gleichung oder quantenchemische Systeme.

Description: We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A.~Cayley in 1845. We prove integrability (understood as $4d$-consistency) of a nonlinear difference equation defined by the $2 \times 2 \times 2$ - hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the $2\times 2\times 2\times 2$ - hyperdeterminant.

Description: The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems.

Description: Since the initial application of mathematical optimisation methods to mine planning in 1965, the Lerchs-Grossmann algorithm for computing the ultimate pit limit, operations researchers have worked on a variety of challenging problems in the area of open pit mining. This thesis focuses on the open pit mining production scheduling problem: Given the discretisation of an orebody as a block model, determine the sequence in which the blocks should be removed from the pit, over the lifespan of the mine, such that the net present value of the mining operation is maximised. In practise, when some material has been removed from the pit, it must be processed further in order to extract the valuable elements contained therein. If the concentration of valuable elements is not sufficiently high, the material is discarded as waste or stockpiled. Realistically-sized block models can contain hundreds of thousands of blocks. A common approach to render these problem instances computationally tractable is the aggregation of blocks to larger scheduling units. The thrust of this thesis is the investigation of a new mixed-integer programming formulation for the open pit mining production scheduling problem, which allows for processing decisions to be made at block level, while the actual mining schedule is still computed at aggregate level. A drawback of this model in its full form is the large number of additional variables needed to model the processing decisions. One main result of this thesis shows how these processing variables can be aggregated efficiently to reduce the problem size significantly, while practically incurring no loss in net present value. The second focus is on the application of lagrangean relaxation to the resource constraints. Using a result of Möhring et al. (2003) for project scheduling, the lagrangean relaxation can be solved efficiently via minimum cut computations in a weighted digraph. Experiments with a bundle algorithm implementation by Helmberg showed how the lagrangean dual can be solved within a small fraction of the time required by standard linear programming algorithms, while yielding practically the same dual bound. Finally, several problem-specific heuristics are presented together with computational results: two greedy sub-MIP start heuristics and a large neighbourhood search heuristic. A combination of a lagrangean-based start heuristic followed by a large neighbourhood search proved to be effective in generating solutions with objective values within a 0.05% gap of the optimum.

Description: Starting from the conservation laws for mass, momentum and energy together with a three species, bulk microphysic model, a model for the interaction of internal gravity waves and deep convective hot towers is derived by using multiscale asymptotic techniques. From the resulting leading order equations, a closed model is obtained by applying weighted averages to the smallscale hot towers without requiring further closure approximations. The resulting model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction of saturated regions on the microscale with two way coupling between the large and small scale. Moisture reduces the effective stability in the model and defines a potential temperature sourceterm related to the net effect of latent heat release or consumption by microscale up- and downdrafts. The dispersion relation and group velocity of the system is analyzed and moisture is found to have several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below which modes turn into evanescent. Further, moisture can cause critical layers. Numerical examples for steadystate and timedependent mountain waves are shown and the effects of moisture on these waves are investigated.

Description: In dieser Arbeit wird ein neuer Ansatz zur Modellierung von thermal signifikanten Gefäßsträngen im Hyperthermie-Kontext betrachtet. Ausgehend von einer Konvektions-Diffusions-Gleichung wird durch Reskalierung des Massenflussterms eine Reduktion des Adergebietes auf eine 1D-Struktur erreicht. Nach numerischen Vorbetrachtungen wird die Grenzgleichung innerhalb einer verallgemeinerten Sobolev-Algebra formuliert. Die Untersuchung der Lösungsfamilie in klassischen Funktionenräumen zeigt, dass deren schwacher Grenzwert die Lösung der korrespondierenden Diffusions-Gleichung ist. Die Diskretisierung einer formalen Grenzgleichung mit Linienstromanteil stellt jedoch eine gute Approximation an die Diskretisierung des ursprünglichen Problems dar, wenn man die lokale Maschenweite an die Gefäßradien koppelt und bei erhöhtem Genauigkeitsbedarf auf ein vollständiges 3D-Modell umschaltet.

Description: Aktuelle Entwicklungen zeigen, dass Peer-to-Peer (P2P) Anwendungen wie Skype oder Bittorrent im Internet immer mehr an Bedeutung gewinnen. In den letzten Jahren hat es einen explosionsartigen Anstieg an Nutzern und Daten in solchen Netzen gegeben. Dabei stellt der eigentliche Dateitransfer zwischen zwei Rechnern kein großes Problem mehr dar und auch der Speicherbedarf für die große Menge an Daten kann durch die Weiterentwicklung der Hardware gut gedeckt werden. Das eigentliche Problem liegt vielmehr darin, den Rechner zu finden, der die gewünschten Daten hat. Client-Server Architekturen, wie zum Beispiel Napster, haben sich als ungünstig herausgestellt. Wenige Server, die eine große Anzahl an Clients bedienen müssen, sind einerseits sehr anfällig gegenüber Angriffen und Ausfällen (Single Point of Failure)und kommen auch nicht mit der ständig wachsenden Anzahl an Nutzern zurecht. Verteilte Hashtabellen (DHT) bieten hier einen guten Lösungsansatz, der mit einer großen Anzahl an Nutzern skaliert und ausfallsicher ist. Andere dezentrale Lösungen, wie zum Beispiel das P2P Netzwerk Gnutella haben zwar das Problem des Single Point of Failure gelöst, jedoch haben sie starke Nachteile bei der Suche nach Keys. Bei einer Suche wird ein Broadcast verwendet (jeder schickt die Anfrage an jeden weiter) und damit ein enormer Netzwerkverkehr erzeugt. In "Why Gnutella Can't Scale. No, Really" wird erklärt, dass eine Suchanfrage bei Standardeinstellungen in der Clientsoftware einen Netzwerkverkehr von 17MB erzeugt. Deswegen wird zusätzlich eine Lösung benötigt, die Keys und Values geordnet verteilt, damit sie gezielt gesucht werden können. Aus diesem Grund beschäftigt sich die folgende Arbeit mit einer völlig dezentralen Architektur, die außerdem eine sinnvolle Platzierung der Keys vornimmt. Die dezentrale Architektur hat den Vorteil, dass die Endgeräte den Hauptteil des Dienstes selbst erbringen und damit jeder zusätzliche Teilnehmer seine eigenen Ressourcen beisteuert. Diese Arbeit präsentiert Chord#, eine dezentrale, skalierbare und selbstorganisierende verteilte Hashtabelle. Chord# wurde ausgewählt, da in dieser Arbeit auch Wert auf Bereichsabfragen gelegt wurde. Diese sind zum Beispiel bei dem Chord Algorithmus nicht möglich, da dieser eine Hashfunktion für die Keys verwendet und somit die Daten zwar gleichmäßig aber unsortiert auf die Teilnehmer verteilt. Es wird in dieser Arbeit gezeigt, dass mit Hilfe von Chord# auch ohne die Hashfunktion gute Ergebnisse erzielt werden. Außerdem können durch den Verzicht auf die Hashfunktion Bereichsabfragen ermöglicht werden. Dafür wird der Chord# Algorithmus in Java implementiert (ca. 1500 Zeilen Code) und in dem Forschungsnetz PlanetLab ausführlich auf Laufzeiten, Instandhaltungskosten und Skalierung getestet.

Description: Recent developments show that peer-to-peer (p2p) applications, such as Skype or Bittorrent have become increasingly important in the internet. Over the last years there has been a rapid growth of both users and data in such networks. However, the actual file transfer between two peers is not really an issue anymore. The same holds true for data storage, since the new hardware grants users enough space to store their data. The real problem is finding the peers that possess the desired data. Client-server architectures like Napster have proven to be ineffective addressing that problem. One or few servers being responsible for many peers are vulnerable to attacks or failures (single point of failure). Additionally, they are unable to cope with the rapidly growing number of peers. Distributed hashtables (DHT) are a good approach to solve these problems, since they scale nicely with large numbers of peers and provide a high tolerance for errors. Other decentralized solutions like the p2p network Gnutella solved the problem of Single Point of Failure but show considerable disadvantages when searching for keys. The peers in Gnutella use a broadcast (sending the message to all peers they know)resulting in massive traffic. According to "Why Gnutella Can't Scale. No, Really.", each search using standard client settings yields 17MB traffc. This calls for a different solution, distributing keys and values to peers quickly and efficiently so they can be found fast. For that reason this thesis focuses on a fully distributed architecture using organized key placement. One major advantage of distributed architecture is the fact, that the peers do most of the work themselves. This way, new peers joining the network add resources to it. This thesis presents Chord#, a scalable, self-organizing and completely decentralized DHT. It has been chosen due to its capability to allow range queries. The regular Chord algorithm does not support range queries, because of the hashfunction it uses to evenly distribute the keys among the peers. This results in similar or logical coherent keys most likely not being close together in the network. This thesis shows Chord# achieving same results as Chord - regarding performance costs - without the hashfunction. In dropping the hashfunction this algorithm allows the use of range queries. The Chord# algorithm is implemented in Java (about 1500 lines of code) and thoroughly tested in the research network PlanetLab. The results are evaluated regarding performance, maintenance and scalability.

Description: One of the biggest impacts on the performance of a Distributed Hash Table (DHT), once established, is its ability to balance load among its nodes. DHTs supporting range queries for example suffer from a potentially huge skew in the distribution of their items since techniques such as consistent hashing can not be applied. Thus explicit load balancing schemes need to be deployed. Several such schemes have been developed and are part of recent research, most of them using only information locally available in order to scale to arbitrary systems. Gossiping techniques however allow the retrieval of fairly good estimates of global information with low overhead. Such information can then be added to existing load balancing algorithms that can use the additional knowledge to improve their performance. Within this thesis several schemes are developed that use global information like the average load and the standard deviation of the load among the nodes to primarily reduce the number of items an algorithm moves to achieve a certain balance. Two novel load balancing algorithms have then been equipped with implementations of those schemes and have been simulated on several scenarios. Most of these variants show better balance results and move far less items than the algorithms they are based on. The best of the developed algorithms achieves a 15-30% better balance and moves only about 50-70% of the number of items its underlying algorithm moves. This variation is also very robust to erroneous estimates and scales linearly with the system size and system load. Further experiments with self-tuning algorithms that set an algorithm’s parameter according to the system’s state show that even more improvements can be gained if additionally applied. Such a variant based on the algorithm described by Karger and Ruhl shows the same balance improvements of 15-30% as the variant above but reduces the number of item movements further to 40-65%.

Description: We present Undercover, a primal heuristic for mixed-integer nonlinear programming (MINLP). The heuristic constructs a mixed-integer linear subproblem (sub-MIP) of a given MINLP by fixing a subset of the variables. We solve a set covering problem to identify a minimal set of variables which need to be fixed in order to linearise each constraint. Subsequently, these variables are fixed to approximate values, e.g. obtained from a linear outer approximation. The resulting sub-MIP is solved by a mixed-integer linear programming solver. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. Although general in nature, the heuristic seems most promising for mixed-integer quadratically constrained programmes (MIQCPs). We present computational results on a general test set of MIQCPs selected from the MINLPLib.

Description: In this paper we investigate the performance of several out-of-the box solvers for mixed-integer quadratically constrained programmes (MIQCPs) on an open pit mine production scheduling problem with mixing constraints. We compare the solvers BARON, Couenne, SBB, and SCIP to a problem-specific algorithm on two different MIQCP formulations. The computational results presented show that general-purpose solvers with no particular knowledge of problem structure are able to nearly match the performance of a hand-crafted algorithm.

Description: Eines der Hauptanliegen bei der Initiierung des Kooperativen Bibliotheksverbundes Berlin-Brandenburg (KOBV) war die Schaffung einer modernen, leistungsfähigen Informationsinfrastruktur unter Einbeziehung möglichst aller Bibliotheken der in ihrer Dichte und Vielfalt in Deutschland einmaligen Bibliothekslandschaft. Sie wurde beim Aufbau des KOBV durch die Wahl des Verbundmodelles mit seinen offenen, integrativen Strukturen befördert. Die Ziele und Strategien des KOBV leiten sich aus dem Grundauftrag der Bibliotheken her, ihre NutzerInnen optimal mit Medien und Informationen zu versorgen. Mit dem KOBV haben die Bibliotheken eine gemeinsame Plattform und ein regionales Netzwerk geschaffen, mit deren Hilfe sie die Informationsinfrastruktur in Berlin und Brandenburg zusammen aufgebaut und grundlegend verbessert haben. Nach rund elf Jahren ist der KOBV in eine neue Phase eingetreten, indem er – unter Wahrung seiner institutionellen Eigenständigkeit – eine Strategische Allianz mit dem Bibliotheksverbund Bayern (BVB) eingegangen ist und die bislang auf die Region bezogene Kooperation der Bibliotheken überregional ausgeweitet hat. Wenn auch die Universalbibliotheken des KOBV in dieser Zusammenarbeit einen Kurswechsel zur zentralen Katalogisierung vollziehen, bedeutet dies für den KOBV insgesamt keinen Paradigmenwechsel: Er bleibt ein dezentraler Verbund und wird sein flexibles technisches Mischkonzept von verteilter und zentraler Datenhaltung fortführen. Dieses lässt den Bibliotheken die Freiheit zu entscheiden, ob sie zentral oder dezentral katalogisieren möchten. Die KOBV-Zentrale, die im KOBV keine Aufgaben in der Katalogisierung wahrnimmt, wird wie bislang allen Mitgliedsbibliotheken die ASP-Dienste und weiteren Angebote gleichermaßen zur Verfügung stellen und die Dienstleistungen für NutzerInnen und Bibliotheken weiter ausbauen. Mit dem vorhandenen Know How, der eingesetzten modernen Technologie und der strategischen Entscheidung, Ressourcen und Kompetenzen mit dem BVB zu bündeln und durch verbundübergreifende arbeitsteilige Verfahren Synergien zu gewinnen, ist der KOBV gut aufgestellt, um die Herausforderungen der kommenden Jahre anzugehen und das Leistungsspektrum der KOBV-Bibliotheken durch die Entwicklung neuer Dienste auszuweiten.

Description: Entwurf und Entwicklung eines eingebetteten Hauptspeicher-Datenbanksystems mit Snapshot-Reads.

Description: Design and implementation of an embedded main memory database with snapshot reads.

Description: We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent processor sharing discipline, where each request receives a service capacity which depends on the actual number of requests in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which provides time reversibility including sojourn times for this system, and their minimal non negative solution gives the LST of the sojourn time $V(\tau)$ of a request with required service time $\tau$. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs, whose minimal non negative solution gives the LST of $V(\tau)$, and which yields linear systems of ODEs for the moments of $V(\tau)$ in the considered neighborhood of zero. Numerical results are presented for the variance of $V(\tau)$. In case of an M/GI/2-PS system, the LST of $V(\tau)$ is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For bounded from below service times, surprisingly simple expressions for the LST and variance of $V(\tau)$ in this neighborhood of zero are derived, which yield in particular the LST and variance of $V(\tau)$ in M/D/2-PS.

Description: Eigentlich war der erste Autor nur zu einem Grußwort zur Tagung „GML² 2009 - Grundfragen Multi¬medialen Lehrens und Lernens“ eingeladen. Daraus wurde ein E-Learning-bezogener Vortrag, der – basierend auf Erfahrungen im Fach Mathematik – einen kritischen Blick auf die E-Learning-Szene in Deutschland wirft und diese mit entsprechenden Aktivitäten weltweit vergleicht. Dies ist die in seinen mathematischen Teilen gekürzte, in den E-Learning-Anteilen ein wenig erweiterte schriftliche Fassung des Vortrags. Der Artikel stammt nicht von E-Learning-Spezialisten sondern von Personen, die sich seit fast zwanzig Jahren mit elektronischer Information und Kommunikation (kurz: IuK) – insbesondere in der Mathematik – beschäftigen. Nach einer Definition von Michael Kerres kennzeichnet der Begriff E-Learning (electronic learning – elektronisch unterstütztes Lernen) alle Formen von Lernen, bei denen digitale Medien für die Präsentation und Distribution von Lernmaterialien und/oder zur Unterstützung zwischenmenschlicher Kommunikation zum Einsatz kommen, siehe z.B. http://de.wikipedia.org/wiki/E-Learning. IuK und E-Learning haben nach dieser Begriffsbildung viele Berührungspunkte. Deswegen wagen wir es, unsere positiven und negativen Erfahrungen im Bereich IuK in diesem Eröffnungsvortrag zu berichten, einige Entwicklungslinien zu vergleichen und eine eigene Kurzversion der Definition von E-Learning (besser E-Teaching and -Learning) voranzustellen: „Lehren und Lernen mit Unterstützung elektronischer Hilfsmittel“.

Description: Das Ziel dieser Arbeit ist die Schaffung einer Zugriffs-Komponente für das Grid-Datenmanagement-System ZIB-DMS, das dessen transparente Einbindung in den Verzeichnisbaum eines Linux-Systems erlaubt. Dazu wird unter Verwendung des FUSE-Rahmenwerkes ein Userspace-Dateisystem mit Anbindung an das ZIB-DMS konzipiert und implementiert. Im Fokus stehen dabei die Abbildung der erweiterten Verwaltungsmechanismen des Systems auf die limitierte Schnittstelle hierarchischer Dateisysteme und die dazu notwendigen Änderungen am ZIB-DMS.

Description: The goal of this work is to create an access component for the Grid data management system ZIB-DMS, that allows a transparent integration into the directory tree of a Linux system. For this purpose the FUSE framework is used to design and implement a userspace file system with connections to the ZIB-DMS. The focus is on the mapping of the extended management mechanisms of the system to the limited interface of hierarchical file systems and the therefore necessary changes to ZIB-DMS.

Description: We present a framework for transactional data access on data stored in a DHT. It allows to atomically read and write items and to run distributed transactions consisting of a sequence of read and write operations on the items. Items are symmetrically replicated in order to achieve durability of data stored in the SON. To provide availability of items despite the unavailability of some replicas, operations on items are quorum-based. They make progress as long as a majority of replicas can be accessed. Our framework processes transactions optimistically with an atomic commit protocol that is based on Paxos atomic commit. We present algorithms for the whole framework with an event based notation. Additionally we discuss the problem of lookup inconsistencies and its implications on the one-copy serializability property of the transaction processing in our framework.

Description: When planning teams for projects with specific goals, employees of a company have to group together so well, that all necessary knowledge for conquering the project’s challenges are met within the member’s skills. A tool that facilitates semantic web technologies can support the team recruiter, who is responsible for chosing the members of the team, in terms of finding the most efficient combinations of the company’s employees based on their expertises.

Description: Telecommunication transport networks consist of a stack of technologically different subnetworks, so-called layers, which are strongly interdependent. For example, one layer may correspond to an Internet (IP) backbone network whose links are realized by lightpath connections in an underlying optical fiber layer. To ensure that the network can fulfill its task of routing all communication requests, the inter-layer dependencies have to be taken into account already in the planning phase of the network. This is particularly important with survivability constraints, where connections in one layer have to be protected against cable cuts or equipment failures in another layer. The traditional sequential planning approach where one layer is optimized after the other cannot properly take care of the inter-layer dependencies; this can only be achieved with an integrated planning of several network layers at the same time. This thesis provides mathematical models and algorithmic techniques for the integrated optimization of two network layers with survivability constraints. We describe a multi-layer network design problem which occurs in various technologies, and model it mathematically using mixed-integer programming (MIP) formulations. The presented models cover many important practical side constraints from different technological contexts. In contrast to previous models from the literature, they can be used to design large two-layer networks with survivability requirements. We discuss modeling alternatives for various aspects of a multi-layer network and compare different routing formulations under multi-layer survivability constraints. We solve our models using a branch-and-cut-and-price approach with various problemspecific enhancements. This includes a presolving technique based on linear programming to reduce the problem size, combinatorial and sub-MIP-based primal heuristics to compute feasible network configurations, cutting planes which take the multi-layer survivability constraints into account to improve the lower bound on the optimal network cost, and column generation to generate flow variables dynamically during the algorithm. We develop techniques to speed up computations in a Benders decomposition approach and compare this approach to the standard formulation with a single MIP. We use the developed techniques to design large survivable two-layer networks by means of linear and integer programming methods. On realistic test instances with up to 67 network nodes and survivability constraints, we investigate the algorithmic impact of our techniques and show how to use them to compute good network configurations with quality guarantees. Most of the smaller test instances with up to 17 nodes can be solved to near-optimality. Moreover, we can compute feasible solutions and dual bounds even for large networks with survivability constraints, which has not been possible before.

Description: In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. We investigate various methods from modern numerical linear algebra to improve the computation speed of the basis updates arising in LPs. The experiments are executed on a large real-world test set. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performance. Using a wide range of LPs we show numerically that after a simple permutation the non-triangular part of the basis matrix is so small, that the whole matrix can be factorized with (relative) fill-in close to the optimum. This permutation has been exploited by simplex practitioners for many years. But to our knowledge no systematic numerical study has been published that demonstrates the effective reduction to a surprisingly small non-triangular problem, even for large scale LPs. For the factorization of the non-triangular part most existing simplex codes use some variant of dynamic Markowitz pivoting, which originated in the late 1950s. We also show numerically that, in terms of fill-in and in the simplex context, dynamic Markowitz is quite consistently superior to other, more recently developed techniques.

Description: We compute expectation values for the solution of the nuclear Schrödinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.

Description: This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.

Description: Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.

Description: Key/value stores which are built on structured overlay networks often lack support for atomic transactions and strong data consistency among replicas. This is unfortunate, because consistency guarantees and transactions would allow a wide range of additional application domains to benefit from the inherent scalability and fault-tolerance of DHTs. The Scalaris key/value store supports strong data consistency and atomic transactions. It uses an enhanced Paxos Commit protocol with only four communication steps rather than six. This improvement was possible by exploiting information from the replica distribution in the DHT. Scalaris enables implementation of more reliable and scalable infrastructure for collaborative Web services that require strong consistency and atomic changes across multiple items.

Description: We consider a system with Poisson arrivals and general service times, where the requests are served according to the State-Dependent Processor Sharing (SDPS) discipline (Cohen's generalized processor sharing discipline), where each request receives a service capacity which depends on the actual number of requests in the system. For this system, denoted by $M/GI/SDPS$, we derive approximations for the squared coefficients of variation of the conditional sojourn time of a request given its service time and of the unconditional sojourn time by means of two-moment fittings of the service times. The approximations are given in terms of the squared coefficients of variation of the conditional and unconditional sojourn time in related $M/D/SDPS$ and $M/M/SDPS$ systems, respectively. The numerical results presented for $M/GI/m-PS$ systems illustrate that the proposed approximations work well.

Description: Gemeinsame Web-Auftritte zu organisieren, die sich über mehrere Institutionen und Fachgebiete erstrecken, ist eine anspruchsvolle und faszinierende Aufgabe, die auf verschiedene Weise gelingen, aber auch scheitern kann. Wer sich daran versucht, tut gut daran, sich über bestimmte Prinzipien und technische Mittel zu informieren, die das fortgeschrittene Web ihm heute bietet. Das Internet, das World Wide Web und das moderne Web 2.0 sind in einer fast zwanzig Jahre dauernden Kollaboration einer globalen Gemeinschaft von Entwicklern und Anwendern entstanden. Es enthält heute eine Fülle sofort einsetzbarer Komponenten, von der „Benutzerdefinierten Google-Suche Beta“ mit Google‘s PageRanking auf ausgewählten Web-Seiten bis hin zum automatisierten Web-Server mit Content-Management für das „Mitmach-Web“. Der Artikel stellt nur eine kleine Auswahl solcher Lösungen vor und macht den Versuch, einige Prinzipien des Web 2.0 so herauszuarbeiten, dass die notwendige Kommunikation zwischen Managern, Technikern, Redakteuren und Organisatoren in der kleinen Kollaboration unterstützt wird. „Kleine Kollaboration“ bedeutet hier, dass es nicht um die globale Vernetzung von technischen Großgeräten der e-Science gehen soll, auch nicht um die Super-Suchmaschine in Europa, sondern um die Unterstützung der Zusammenarbeit und Kommunikation von Wissenschaftlern und Museumsfachleuten mit Ihren Nutzern.

Description: We consider a system with Poisson arrivals and i.i.d. service times and where the requests are served according to the state-dependent (Cohen's generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive asymptotically tight upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize corresponding results, recently given for the single-server processor sharing system by Cheung et al. and for the state-dependent processor sharing system with exponential service times by the authors. Analogous results hold for the waiting times.

Description: The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of $\frac{1+\sqrt{2}}{2}$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm.

Description: This thesis introduces the novel paradigm of "constraint integer programming" (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.

Description: Diese Arbeit stellt einen integrierten Ansatz aus "Constraint Programming" (CP) und Gemischt-Ganzzahliger Programmierung ("Mixed Integer Programming", MIP) vor, den wir "Constraint Integer Programming" (CIP) nennen. Sowohl Modellierungs- als auch Lösungstechniken beider Felder fließen in den neuen integrierten Ansatz ein, um die unterschiedlichen Stärken der beiden Gebiete zu kombinieren. Als weiteren Beitrag stellen wir der wissenschaftlichen Gemeinschaft die Software SCIP zur Verfügung, die ein Framework für Constraint Integer Programming darstellt und zusätzlich Techniken des SAT-Lösens beinhaltet. SCIP ist im Source Code für akademische und nicht-kommerzielle Zwecke frei erhältlich. Unser Ansatz des Constraint Integer Programming ist eine Verallgemeinerung von MIP, die zusätzlich die Verwendung beliebiger Constraints erlaubt, solange sich diese durch lineare Bedingungen ausdrücken lassen falls alle ganzzahligen Variablen auf feste Werte eingestellt sind. Die Constraints werden von einer beliebigen Kombination aus CP- und MIP-Techniken behandelt. Dies beinhaltet insbesondere die "Domain Propagation", die Relaxierung der Constraints durch lineare Ungleichungen, sowie die Verstärkung der Relaxierung durch dynamisch generierte Schnittebenen. Die derzeitige Version von SCIP enthält alle Komponenten, die für das effiziente Lösen von Gemischt-Ganzzahligen Programmen benötigt werden. Die vorliegende Arbeit liefert eine ausführliche Beschreibung dieser Komponenten und bewertet verschiedene Varianten in Hinblick auf ihren Einfluß auf das Gesamt-Lösungsverhalten anhand von aufwendigen praktischen Experimenten. Dabei wird besonders auf die algorithmischen Aspekte eingegangen. Ein weiterer Hauptteil der Arbeit befasst sich mit der Chip-Design-Verifikation, die ein wichtiges Thema innerhalb des Fachgebiets der "Electronic Design Automation" darstellt. Chip-Hersteller müssen sicherstellen, dass der logische Entwurf einer Schaltung der gegebenen Spezifikation entspricht. Andernfalls würde der Chip fehlerhaftes Verhalten aufweisen, dass zu Fehlfunktionen innerhalb des Gerätes führen kann, in dem der Chip verwendet wird. Ein wichtiges Teilproblem in diesem Feld ist das Eigenschafts-Verifikations-Problem, bei dem geprüft wird, ob der gegebene Schaltkreisentwurf eine gewünschte Eigenschaft aufweist. Wir zeigen, wie dieses Problem als Constraint Integer Program modelliert werden kann und geben eine Reihe von problemspezifischen Algorithmen an, die die Struktur der einzelnen Constraints und der Gesamtschaltung ausnutzen. Testrechnungen auf Industrie-Beispielen vergleichen unseren Ansatz mit den bisher verwendeten SAT-Techniken und belegen den Erfolg unserer Methode.

Description: In this paper we investigate the fare planning model for public transport, which consists in designing a system of fares maximizing the revenue. We discuss a discrete choice model in which passengers choose between different travel alternatives to express the demand as a function of fares. Furthermore, we give a computational example for the city of Potsdam and discuss some theoretical aspects.

Description: This extended abstract is about algorithms for controlling elevator systems employing destination hall calls, i.e. the passenger provides his destination floor when calling an elevator. We present the first exact algorithm for controlling a group of elevators and report on simulation results indicating that destination hall call systems outperform conventional systems.

Description: The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of interest. Finally, the efficiency of the error estimator and generated meshes are demonstrated on numerical examples.

Description: The paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Among the numerical integrators, interest focuses on the contact-stabilized Newmark method recently suggested by Deuflhard et al., which is compared to the classical Newmark method and an improved energy dissipative version due to Kane et al. In the absence of contact, any such variant is equivalent to the Störmer-Verlet scheme, which is well-known to have consistency order 2. In the presence of contact, however, the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact. Surprisingly, the question of consistency in the constrained situation has not been solved yet. The present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors. The corresponding estimation of the local discretization error requires the bounded total variation of the solution. The results have consequences for the construction of an adaptive timestep control, which will be worked out subsequently in a forthcoming paper.

Description: The mathematical treatment of planning problems in public transit has made significant advances in the last decade. Among others, the classical problems of vehicle and crew scheduling can nowadays be solved on a routine basis using combinatorial optimization methods. This is not yet the case for problems that pertain to the design of public transit networks, and for the problems of operations control that address the implementation of a schedule in the presence of disturbances. The article gives a sketch of the state and important developments in these areas, and it addresses important challenges. The vision is that mathematical tools of computer aided scheduling (CAS) will soon play a similar role in the design and operation of public transport systems as CAD systems in manufacturing.

Description: Die mathematische Behandlung von Planungsproblemen im öffentlichen Verkehr hat im letzten Jahrzehnt große Fortschritte gemacht. Klassische Probleme wie die Umlauf- und die Dienstplanung können heutzutage routinemäßig mit kombinatorischen Optimierungsmethoden gelöst werden. Die Behandlung von Problemen der Angebotsplanung und der Betriebssteuerung sind dagegen noch nicht ganz auf diesem Stand. Dieser Artikel gibt einen Überblick über den Stand der Forschung, über wichtige Entwicklungen und einige Herausforderungen in diesem Gebiet. Die Vision ist, dass mathematische Planungswerkzeuge im öffentlichen Verkehr (Computer Aided Scheduling, CAS) in Zukunft eine ähnliche Rolle spielen werden wie CAD-Systeme in der industriellen Fertigung.

Description: The reconstruction of geometric shapes plays an important role in many biomedical applications. One example is the patient-specific, computer-aided planning of complex interventions, which requires the generation of explicitly represented geometric models of anatomical structures from medical image data. Only solutions that require minimal interaction by medical personnel are likely to enter clinical routine. Another example is the planning of surgical corrections of deformities where the target shape is unknown. Surgeons are often forced to resort to subjective criteria. These applications still pose highly challenging reconstruction problems, which are addressed in this thesis. The fundamental hypothesis, pursued in this thesis, is that the problems can be solved by incorporating a-priori knowledge about shape and other application-specific characteristics. Here, we focus mainly on the aspect of geometric shape analysis. The basic idea is to capture the most essential variations of a certain class of geometric objects via statistical shape models, which model typical features contained in a given population, and restrict the outcome of a reconstruction algorithm (more or less) to the space spanned by such models. A fundamental prerequisite for performing statistical shape analysis on a set of different objects is the identification of corresponding points on their associated surfaces. This problem is particularly difficult to solve if the shapes stem from different individuals. The reason lies in the basic difficulty of defining suitable measures of similarity. In this thesis, we divide the correspondence problem into feature and non-feature matching. The feature part depends on the application, while the non-feature part can be characterized by a purely geometric description. We propose two different approaches. The first approach has proved useful in many applications. Yet, it suffers from some practical limitations and does not yield a measure of similarity. Our second, variational, approach is designed to overcome these limitations. In it, we propose to minimize an invariant stretching measure, constrained by previously computed features. An important property, which sets our method apart from previous work, is that it does not require the computation of a global surface parameterization.

Description: Basierend auf einem vorhandenen Ansatz zur Einführung von anisotropen Tetraedern im Randbereich eines reinen Tetraedergitters wird ein Gittergenerator für hybride Gitter implementiert. Das hybride Gitter besteht in Randnähe primär aus anisotropen Prismen und im Inneren der Geometrie aus isotropen Tetraedern. Eine erhöhte Auflösung im Randbereich soll zu besseren Ergebnissen von numerischen Strömungssimulationen führen, für welche eine problemangepasste Diskretisierung des zu untersuchenden Gebietes benötigt wird. In dem zuvor genannten Ansatz wird eine Reihe von Übergangselementen vorgeschlagen, die an scharfen Kanten der Oberfläche platziert werden sollen. Im Rahmen dieser Diplomarbeit wird die Idee der Übergangselemente aufgegriffen und bei hybriden Gittern eingesetzt, um auch komplexe Eingabegeometrien vergittern zu können. Der ursprüngliche Gittergenerierungprozess wird überarbeitet und erweitert. Eine neue Menge an Übergangselementen wird eingeführt, es werden gekrümmte Extrusionsvektoren verwendet und es wird die Auswertung der medialen Oberfläche vorgenommen, um Überschneidungen im hybriden Gitter zu vermeiden. Der Gittergenerator wird als Modul in das Visualisierungs- und Analyseprogramm Amira implementiert und die erstellten hybriden Gitter werden auf ihre Elementqualität und die Güte der Strömungssimulationsergebnisse hin überprüft.

Description: Based on an existing approach for the introduction of anisotropic tetrahedra near the surface boundary of a tetrahedral grid a grid generator for hybrid grids is implemented. The hybrid grid consists near the surface boundary primarily of anisotropic prisms and inside the geometry of isotropic tetrahedra. An increased resolution near the boundary should lead to better results of numerical flow simulations, which needs a problem specific discretization of the analyzed domain. In the aforementioned approach a set of transition elements is suggested, which should be placed at sharp surface corners. As a part of this diploma thesis the concept of using transition elements is applied for creating hybrid grids even for very complex input geometries. The initial grid generation process is revised and enhanced. A new set of transition elements is introduced, curved extrusion vectors are used and the medial surface is evaluated to avoid intersections in the hybrid grid. The grid generator is implemented as a module for the visualization and analysis tool Amira and the element quality of the generated hybrid grids and the quality of flow simulations performed on the grids are tested.

Description: Im Kooperativen Bibliotheksverbund Berlin-Brandenburg (KOBV) wird für die automatisierte Fernleihe der Zentrale-Fernleihserver (ZFL-Server) der Firma Sisis eingesetzt. Die Software ist in der KOBV-Zentrale installiert. Der ZFL-Server dient im KOBV sowohl für die Bestellung von Monographien als auch für die Bestellung von Aufsatzkopien aus Zeitschriften. Prinzipiell gibt es zwei Verfahren, mit denen sich Bibliotheken an der automatisierten Fernleihe beteiligen können: das E-Mail-Verfahren und das SLNP-Verfahren. Auf beide wird im Handbuch eingegangen. Die automatisierte Fernleihe wurde im KOBV eingeführt, um die Fernleihe für die Benutzer zu beschleunigen, das Verfahren für die Bibliotheksmitarbeiter zu vereinfachen und den Arbeitsaufwand zu reduzieren. Sie basiert darauf, dass eine Bestellung anhand eines gefundenen Treffers ausgelöst wird – d.h. die bibliographischen Daten sind bereits verifiziert und in einem Katalog nachgewiesen. Anschließend wird die Bestellung über den ZFL-Server automatisch ausgeführt und verwaltet – sowohl in der regionalen KOBV-Fernleihe als auch in der verbundübergreifenden Fernleihe mit den deutschen Bibliotheksverbünden. Der ZFL-Server besteht aus verschiedenen technischen Komponenten. Eine dieser Komponenten ist das Bibliothekskonto, eine Internetanwendung, in der die Bestellverwaltung des ZFL-Servers für die Bibliotheksbediensteten transparent abläuft. Dazu hat jede Bibliothek im Bibliothekskonto eine eigene, Passwort-geschützte Dienstoberfläche. Im Laufe des Jahres 2009 hat die KOBV-Zentrale das Bibliothekskonto grundlegend überarbeitet; die neue Version wurde im September 2009 freigegeben. Neben der Überabeitung des Interfaces – so wird den Bibliotheken auf der Startseite nun eine Übersicht ihrer laufenden Bestellungen angezeigt und dient als direkter Einstieg in die Bearbeitung – wurde das Bibliothekskonto um folgende Funktionen erweitert: Bestellung zurücklegen (HOLD), Vormerkungen, Bestellungen zur Anfrage, Abbruch des Leitweges (auch verbundübergreifend), erweiterte Kommentarfunktion, Bestellnummernsuche in allen Verbünden. Das Handbuch, das die Vorgänge der Bestellverwaltung im Bibliothekskonto beschreibt, wurde in der nun vorliegenden 3. Auflage um die Beschreibung der neuen Funktionen ergänzt. An dieser Stelle ein Dank an die Kolleginnen und Kollegen aus den KOBV-Bibliotheken – Frau Bruske (UB der Freien Universität Berlin), Frau Ebert (UB der Europa-Universität Viadrina Frankfurt (Oder)), Frau Preuß (UB der Technischen Universität Berlin) und Herrn Ringmayer (Zentral- und Landesbibliothek Berlin) – für die tatkräftige Unterstützung bei der Entwicklung der neuen Funktionen.

Description: We propose a variant of the control reduced interior point method for the solution of state constrained problems. We show convergence of the corresponding interior point pathfollowing algorithm in function space. Morever, we provide error bounds for the iterates.

Description: This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper.

Description: This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same.

Description: In this paper, we study the efficiency of Nash equilibria for a sequence of nonatomic routing games. We assume that the games are played consecutively in time in an online fashion: by the time of playing game $i$, future games $i+1,\dots,n$ are not known, and, once players of game $i$ are in equilibrium, their corresponding strategies and costs remain fixed. Given a sequence of games, the cost for the sequence of Nash equilibria is defined as the sum of the cost of each game. We analyze the efficiency of a sequence of Nash equilibria in terms of competitive analysis arising in the online optimization field. Our main result states that the online algorithm $\sl {SeqNash}$ consisting of the sequence of Nash equilibria is $\frac{4n}{2+n}$-competitive for affine linear latency functions. For $n=1$, this result contains the bound on the price of anarchy of $\frac{4}{3}$ for affine linear latency functions of Roughgarden and Tardos [2002] as a special case. Furthermore, we analyze a problem variant with a modified cost function that reflects the total congestion cost, when all games have been played. In this case, we prove an upper bound of $\frac{4n}{2+n}$ on the competitive ratio of $\sl {SeqNash}$. We further prove a lower bound of $\frac{3n-2}{n}$ of $\sl {SeqNash}$ showing that for $n=2$ our upper bound is tight.

Description: To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing $N$ steps requires only $O(N\log N)$ operations and $O(\log N)$ active memory, in place of $O(N^2)$ operations and $O(N)$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schrödinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law.

Description: This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.

Description: The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle).

Description: The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branch-and-cut tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving this kind of symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branch-and-cut tree, removes redundant parts of the tree produced by the above mentioned permutations. The method relies on certain polyhedra, called orbitopes, which have been investigated in (Kaibel and Pfetsch (2006)). However, it does not add inequalities to the model, and thus, it does not increase the difficulty of solving the linear programming relaxations. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem motivated from frequency planning in mobile telecommunication networks.

Description: In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph $D=(V,A)$ and a set $K$ of directed commodities, an USPR is a set of flow paths $\Phi_{(s,t)}$, $(s,t)\in K$, such that there exists a metric $\lambda=(\lambda_a)\in \mathbb{Z}^A_+$ with respect to which each $\Phi_{(s,t)}$ is the unique shortest $(s,t)$-path. In the \textsc{Min-Con-USPR} problem, we seek for an USPR that minimizes the maximum congestion over all arcs. We show that this problem is hard to approximate within a factor of $\mathcal{O}(|V|^{1-\epsilon})$, but easily approximable within min$(|A|,|K|)$ in general and within $\mathcal{O}(1)$ if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of $\Omega(|V|^2)$ larger than that achievable by unsplittable flow routing or by shortest multi-path routing, and a factor of $\Omega(|V|)$ larger than by unsplittable source-invariant routing. In the CAP-USPR problem, we seek for a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is $\mathcal{NP}$-hard to approximate within $2-\epsilon$ (even in the undirected case), and we devise approximation algorithms for various special cases. The fixed charge network design problem \textsc{Cap-USPR}, where the task is to find a minimum cost subgraph of $D$ whose fixed arc capacities admit an USPR of the commodities, is shown to be $\mathcal{NPO}$-complete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems.

Description: In this paper, we investigate the connection availabilities for the new protection scheme Demand-wise Shared Protection (DSP) and describe an appropriate approach for their computation. The exemplary case study on two realistic network scenarios shows that in most cases the availabilities for DSP are comparable with that for 1+1 path protection and better than in case of shared path protection.

Description: THESEUS, the ZIB threading environment, is a parallel implementation of a protein threading based on a multi-queued branch-and-bound optimal search algorithm to find the best sequence-to-structure alignment through a library of template structures. THESEUS uses a template core model based on secondary structure definition and a scoring function based on knowledge-based potentials reflecting pairwise interactions and the chemical environment, as well as pseudo energies for homology detection, loop alignment, and secondary structure matching. The threading core is implemented in C++ as a SPMD parallization architecture using MPI for communication. The environment is designed for generic testing of different scoring functions, e.g. different secondary structure prediction terms, different scoring matrices and information derived from multiple sequence alignments. A validaton of the structure prediction results has been done on the basis of standard threading benchmark sets. THESEUS successfully participated in the 6th Critical Assessment of Techniques for Protein Structure Prediction (CASP) 2004.

Description: We consider a multi-queue multi-server system with $n$ servers (processors) and $m$ queues. At the system there arrives a stationary and ergodic stream of $m$ different types of requests with service requirements which are served according to the following $k$-limited head of the line processor sharing discipline: The first $k$ requests at the head of the $m$ queues are served in processor sharing by the $n$ processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes' monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the $m$ separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of $n$=$k$=1.

Description: In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled.

Description: "`Volkssport Sudoku"' titelt der Stern in seiner Ausgabe vom 24. Mai2006. In der Tat traut sich derzeit kaum noch eine Zeitung, ohne Sudoku zu erscheinen. Die Begeisterung am Lösen dieser Zahlenrätsel offenbart eine unvermutete Freude am algorithmischen Arbeiten. Mathematisch kann man Sudokus als lineare diophantische Gleichungssysteme mit Nichtnegativitätsbedingungen formulieren. Solche ganzzahligen linearen Programme sind die wichtigsten Modellierungswerkzeuge in zahlreichen Anwendungsgebieten wie z.B. der Optimierung von Telekommunikations- und Verkehrsnetzen. Moderne Verfahren zur Lösung dieser Optimierungsprobleme sind durch Sudokus allerdings deutlich weniger zu beeindrucken als Zeitungsleser.

Description: This article surveys mathematical models and methods used for physical PCB layout, i.e., component placement and wire routing. The main concepts are briefly described together with relevant references.

Description: We study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining the routing weights. We discuss an online algorithm that routes each commodity by minimizing a convex cost function that depends on the demands that are previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is $4K/2+K$-competitive, where $K$ is the number of commodities. For the parallel arc case this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.

Description: Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs $G$ where the stable set polytope STAB$(G)$ coincides with the clique constraint stable set polytope QSTAB$(G)$. For all imperfect graphs STAB$(G) \subset$ QSTAB$(G)$ holds and, therefore, it is natural to measure imperfection in terms of the difference between STAB$(G)$ and QSTAB$(G)$. Several concepts have been developed in this direction, for instance the dilation ratio of STAB$(G)$ and QSTAB$(G)$ which is equivalent to the imperfection ratio imp$(G)$ of $G$. To determine imp$(G)$, both knowledge on the facets of STAB$(G)$ and the extreme points of QSTAB$(G)$ is required. The anti-blocking theory of polyhedra yields all {\em dominating} extreme points of QSTAB$(G)$, provided a complete description of the facets of STAB$(\overline G)$ is known. As this is typically not the case, we extend the result on anti-blocking polyhedra to a {\em complete} characterization of the extreme points of QSTAB$(G)$ by establishing a 1-1 correspondence to the facet-defining subgraphs of $\overline G$. We discuss several consequences, in particular, we give alternative proofs of several famous results.

Description: We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time $O^\ast(2^n)$. This algorithm is based on the old dynamic programming method introduced by Held and Karp for the {\sc Tra veling Salesman} problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space use d by the algorithm is an important factor to what input sizes the algorithm is effective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In this direction we give a simple $O^\ast(4^n)$ al gorithm that requires {\em polynomial} space. We also show that with a more complicated algorithm, using balanced separators, {\sc Treewidth} can be computed in $O^\ast(2.9512^n)$ time and polynomial space.

Description: The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.

Description: Das deutschsprachige Bibliothekswesen verfügt mit den \glqq Regeln für den Schlagwortkatalog \grqq (RSWK) unter Verwendung der \glqq Schlagwortnormdatei \grqq (SWD) über ein Instrumentarium, welches zusammen mit einem \glqq Faceted Browsing \grqq das bisher bestehende Angebot für ein Information Retrieval optimal ergänzen kann. Die Verbindung zwischen Standardvokabular (SWD) und Kettenbildung (RSWK) einerseits und eine nach Facetten-Eigenschaften gegliederte Navigation andererseits unterstützt bestmöglich eine inhaltlich bezogene Recherche. Die Stärken und Schwächen der RSWK/SWD werden erörtert und auch Klassifikationen (DDC und RVK) als mögliche Facetten diskutiert.

Description: A lot of problems arising in Combinatorial Optimization and Operations Research can be formulated as Mixed Integer Programs (MIP). Although MIP-solving is an NP-hard optimization problem, many practically relevant instances can be solved in reasonable time. In modern MIP-solvers like the branch-cut-and-price-framework SCIP, primal heuristics play a major role in finding and improving feasible solutions at the early steps of the solution process. This helps to reduce the overall computational effort, guides the remaining search process, and proves the feasibility of the MIP model. Furthermore, a heuristic solution with a small gap to optimality often is sufficient in practice. We investigate 16 different heuristics, all of which are available in SCIP. Four of them arise from the literature of the last decade, nine are specific implementations of general heuristic ideas, three have been newly developed. We present an improved version of the feasibility pump heuristic by Fischetti et al., which in experiments produced solutions with only a third of the optimality gap compared to the original version. Furthermore, we introduce two new Large Neighborhood Search (LNS) heuristics. Crossover is an LNS improvement heuristic making use of similarities of diverse MIP solutions to generate new incumbent solutions. RENS is an LNS rounding heuristic which evaluates the space of all possible roundings of a fractional LP-solution. This heuristic makes it possible to determine whether a point can be rounded to an integer solution and which is the best possible rounding. We conclude with a computational comparison of all described heuristics. It points out that a single heuristic on its own has only a slight impact on the overall performance of SCIP, but the combination of all of them reduces the running time by a factor of two compared to a version without any heuristics.

Description: We present a finite volume method for the solution of the two-dimensional Poisson equation $ \nabla\cdot( \beta( {\mbox{\boldmath $x$}}) \nabla u({\mbox{\boldmath $x$}})) = f(\mbox{\boldmath $x$}) $ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution $u({\mbox{\boldmath $x$})$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the $L^\infty$ and $L^2$ norm.

Description: In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.

Description: The concept of jump system, introduced by Buchet and Cunningham (1995), is a set of integer points with a certain exchange property. In this paper, we discuss several linear and convex optimization problems on jump systems and show that these problems can be solved in polynomial time under the assumption that a membership oracle for a jump system is available. We firstly present a polynomial-time implementation of the greedy algorithm for the minimization of a linear function. We then consider the minimization of a separable-convex function on a jump system, and propose the first polynomial-time algorithm for this problem. The algorithm is based on the domain reduction approach developed in Shioura (1998). We finally consider the concept of M-convex functions on constant-parity jump systems which has been recently proposed by Murota (2006). It is shown that the minimization of an M-convex function can be solved in polynomial time by the domain reduction approach.

Description: We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem. We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group. Our main results are complete linear inequality descriptions of these polytopes by facet-defining inequalities. For the cyclic group case, the descriptions turn out to be totally unimodular, while for the symmetric group case, both the description and the proof are more involved. The associated separation problems can be solved in linear time.

Description: The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an $\varepsilon$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.

Description: Wir beschäftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt.

Description: Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.

Description: The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we analyze the complexity of the problem, its relation to the Shortest Path Problem, and the impact of the underlying machine/computation model.

Description: We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lov\´{a}sz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of highly connected, highly symmetric manifolds.

Description: We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.

Description: Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.

Description: We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak convergence of the iterative scheme. In certain cases, i.e. for special families of convex constraints, weak convergence implies norm convergence. The presented approach covers a wide range of problems, e.g. Besov- or BV-restoration for which we present also numerical experiments in the context of image processing.

Description: Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.

Description: \noindent We give a partial description of the $(s,t)-p$-path polytope of a directed graph $D$ which is the convex hull of the incidence vectors of simple directed $(s,t)$-paths in $D$ of length $p$. First, we point out how the $(s,t)-p$-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for the $p$-cycle polytope, that is, the convex hull of the incidence vectors of simple cycles of length $p$ in $D$. We give necessary and sufficient conditions for these inequalities to be facet defining. Furthermore, we consider a class of inequalities that has been identifie d to be valid for $(s,t)$-paths of cardinality at most $p$. Finally, we transfer the results to related polytopes, in particular, the undirected counterpart of the $(s,t)-p$-path polytope.

Description: The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional $L^2$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).

Description: We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.

Description: The concept of L##-convexity is introduced by Fujishige--Murota (2000) as a discrete convexity for functions defined over the integer lattice. The main aim of this note is to understand the difference of the two algorithms for L##-convex function minimization: Murota's steepest descent algorithm (2003) and Kolmogorov's primal algorithm (2005).

Description: In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.

Description: This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most~8\% above a lower bound on optimal RMG utilization.

Description: We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.

Description: We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.

Description: We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2 x S^1$ and 615 triangulations of the twisted sphere product $S^2 \underline{x} S^1$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.

Description: Adaptive numerical methods in time and space are introduced and studied for linear poroelastic models in two and three space dimensions. We present equivalent models for linear poroelasticity and choose both the {\em displacement--pressure} and the {\em stress--pressure} formulation for our computations. Their discretizations are provided by means of linearly implicit schemes in time and linear finite elements in space. Our concept of adaptivity opens a way to a fast and reliable simulation of different loading cases defined by corresponding boundary conditions. We present some examples using our code {\sf Kardos} and show that the method works efficiently. In particular, it could be used in the simulation of some bone healing models.

Description: During the last few years more and more functionalities of RNA have been discovered that were previously thought of being carried out by proteins alone. One of the most striking discoveries was the de tection of microRNAs, a class of noncoding RNAs that play an important role in post-transcriptional gene regulation. Large-scale analyses are needed for the still increasingly growing amount of sequen ce data derived from new experimental technologies. In this paper we present a framework for the detection of the distinctive precursor structure of microRNAS that is based on the well-known Smith-Wat erman algorithm and various filtering steps. We conducted experiments on real genomic data and we found several new putative hits for microRNA precursor structures.

Description: Wir erleben zu Beginn des aufkommenden Informationszeitalters mit dem Siegeszug von Google und anderen Internet-Technologien einen Wandel im Verhalten von Wissenschaftlern und Studenten, der mit dem Einsatz von {\sl Google Scholar} und {\sl Google Book Search} einen Paradigmenwechsel für Bibliotheken und Informationsversorger gleichkommt. Der Artikel untersucht die technischen Hintergründe für den Erfolg dieser besonderen Art des Information Retrievals: Fulltext Indexing und Citation Ranking als besondere Form des Information Minig. Er diskutiert Stärken und auch Schwächen des Google-Ansatzes. Der Autor stellt sich auch der Frage, unter welchen Bedingungen es möglich ist, ein zu {\sl Google Scholar} und der {\sl Google Book Search} konkurrenzfähiges Retrieval in der Landschaft der Bibliotheken und Bibliotheksverbünde zu entrichten. Die These ist, dass dieses unter Einsatz des {\sl Open Source} Indexierers {\sl Lucene} und des Web-Robots {\sl Nutch} möglich ist. Bibliotheken können durch gezielten Einsatz solcher Internet-Technologien dem Nutzer die Leistungen, welche Google uns mit seinen Tools im {\sl Visible Web} und mit Referenzen auf {\sl Citations} in der Welt der Literatur zur Verfügung stellt, in vergleichbarer Art auch für ihre eigenen durch Lizenzen geschützten digitalen Journale und ihre speziellen lokal verfügbaren Ressourcen, auf die Internet-Suchmaschinen keine Zugriff haben, anbieten. Es besteht die Hoffnung, dass Nutzer dann nicht - wie in einer kürzlichen Studie des OCLC konstatiert - überwiegend im Internet verbleiben, sondern bei ihrer Suche auch den Weg zu den Angeboten der örtlichen Bibliothek attraktiv finden.