Library

Description: A set of vertices $S\subseteq V$ is called a safe separator for treewidth, if $S$ is a separator of $G$, and the treewidth of $G$ equals the maximum of the treewidth over all connected components $W$ of $G-S$ of the graph, obtained by making $S$ a clique in the subgraph of $G$, induced by $W\cup S$. We show that such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidth. We give several sufficient conditions for separators to be safe, allowing such separators, if existing, to be found in polynomial time. In particular, every minimal separator of size one or two is safe, every minimal separator of size three that does not split off a component with only one vertex is safe, and every minimal separator that is an almost clique is safe; an almost clique is a set of vertices $W$ such that there is a $v\in W$ with $W-\{v\}$ a clique. We report on experiments that show significant reductions of instance sizes for graphs from proba! bilistic networks and frequency assignment.

Description: A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short step pathfollowing method is established.

Description: We explicitly construct small triangulations for a number of well-known $3$-dimensional manifolds and give a brief outline of some aspects of the underlying theory of $3$-manifolds and its historical development.

Description: Peer-to-Peer (P2P) Systeme werden u.a. zur Verwaltung von großen Datenmengen benutzt, die auf verschiedene Rechner verteilt sind. Benutzern soll damit der Zugriff auf Daten innerhalb des Systems leicht ermöglicht werden. Damit in P2P Systemen die Daten effizient verteilt und gesucht werden können, existieren Distributed Hash Tables. Distributed Hash Tables (DHT) sind eine Methode, um globale Informationen persistent speichern zu können. Der Wertebereich der Hashfunktion, welche die zu veröffentlichenden Einträge auf Werte abbildet, wird in Abschnitte aufgeteilt, die einzelnen Knoten zugeteilt werden. Die meisten DHTs haben aber ein Problem bei der Verteilung der Last. Die verschiedenen DHT Systeme beruhen meist auf einem identischen Ansatz der Lastverteilung. Die Last wird nur mit Hilfe einer Hashfunktion verteilt. Es wird davon ausgegangen, dass diese Funktion die Last gleichmäßig verteilt. Im Rahmen dieser Arbeit wurde ein Verfahren zur Last Verteilung entwickelt, simuliert und implementiert. Bei dem Verfahren wird die Last wie bei der Verteilung von Wärme an die Umgebung abgegeben. Es wird mit existierenden Lastbalancierungsalgorithmen verglichen. Mit diesem neuen Verfahren ist es möglich, Last in DHTs besser zu verteilen ohne große Änderungen an den DHTs vorzunehmen. Es wird gezeigt, wie mit dem Verfahren zusätzlich die Fehlertoleranz des P2P Systems erhöht werden kann.

Description: One of the many uses of Peer-to-Peer (P2P) systems is the administration of large data sets that are distributed across different computers, with the goal of facilitating user access to files within the system. Distributed Hash Tables (DHT) are designed to enable the efficient distribution and search of files, by allowing global information to be persistently stored. The range of values of the hash function (the possible entries in the published hash table) are assigned to individual nodes. Most DHTs, however, have a problem with load distribution. The various DHT systems usually operate by distributing load equally among nodes. Thus the load is distributed using the help of the hash function. One assumes this function distributes the load evenly. In the context of this work a method of distributing load has been developed, simulated and implemented. With this method load is transferred in a fashion analogous to the dissipation of heat into the environment. Comparisons with existing algorithms for load balancing are drawn. With the new procedure it is possible to better distribute load in DHTs without requiring major changes to the DHTs themselves. It is shown that with the procedure the fault tolerance of P2P systems may also be increased.

Description: The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.

Description: In this paper, a new shared protection mechanism for meshed optical networks is presented. Significant network design cost reductions can be achieved in comparison to the well-known 1+1 protection scheme. Demand-wise Shared Protection (DSP) bases on the diversification of demand routings and exploits the network connectivity to restrict the number of backup lightpaths needed to provide the desired level of prorection. Computational experiments approve the benefits of the concept DSP for cost efficient optical network designs.

Description: The correlation of the inner architecture of bone and its functional loading was already stated by Wolff in 1892. Our objective is to demonstrate this interdependence in the case of the human mandible. For this purpose, stress/strain profiles occuring at a human lateral bite were simulated. Additionally, by a combination of computer graphics modules, a three--dimensional volumetric visualization of bone mineral density could be given. Qualitative correspondences between the density profile of the jaw and the simulated stress/strain profiles could be pointed out. In the long run, this might enable the use of the simulation for diagnosis and prognosis. The solution of the underlying partial differential equations describing linear elastic material behaviour was provided by an adaptive finite element method. Estimates of the discretization errors, local grid refinement, and multilevel techniques guaranteed the reliability and efficiency of the method.

Description: UMTS is a 3rd generation mobile telecommunication system which enables multi-service and multi-bit rate communication going beyond the possibilities of previous systems. The simulator MoDySim models UMTS in great detail. Characteristics of UMTS such as soft hand-over and the interdependency of load and capacity among neighbouring cells are challenges for the parallelisation of such a system. In this paper we explain how the software was parallelised and present performance results of a UMTS simulation for the city of Berlin.

Description: We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose the Hybrid Monte Carlo algorithm was used and an explicit symmetry-breaking source term $h\bar{\psi} i \gamma_{5} \tau^{3}\psi$ was added to the Wilson fermion action. The order parameter $\langle\bar{\psi}i\gamma_{5}\tau^{3}\psi\rangle$ was studied at several values of $(\beta,\kappa,h)$ on lattices of sizes $4^4$ to $12^4$. Our largest lattices can be considered as infintely large allowing to extrapolate to $h=0$. The existence of a parity-flavor-breaking phase can be confirmed at $\beta=4.0$ and $\beta=4.3$ while we find no sign of parity-flavor-breaking at $\beta=4.6$ and $\beta=5.0$.

Description: In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplicial struture this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplicial structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this kind of approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs.

Description: The Web of the future will provide a huge amount of information. We need better ways for dealing with and managing the information. A qualified semantic annotation of the information plays a key role for the Web of the future. This article gives an overview about the efforts of the mathematical community to build up a distributed and open information and communication system for mathematics: the Math-Net. The Math-Net Initiative has developed metadata schemas for some classes of Web resources which are relevant in mathematics. Math-Net Services process this information and enable the user to efficiently search and access the information.

Description: In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.

Description: Zeitschriften und andere Medien werden in wachsendem Maße elektronisch publiziert. Hier entsteht für die Bibliotheken, welche diese Online-Publikationen ihren Lesern zur Verfügung stellen, ein neuer Bereich der Informationsvermittlung. Mit dem aufkommenden Standard der OpenURL ergeben sich neue Möglichkeiten, dem Benutzer weiterführende Links und Dienste anzubieten. Das Document-Linking-System SFX der Firma Ex Libris ist die erste und bekannteste Anwendung, die ein Managementsystem fr die Auswertung der OpenURL implementiert. Im Rahmen eines Projektes hat die Zentrale des Kooperativen Bibliotheksverbundes Berlin-Brandenburg (KOBV) eine Evaluation von SFX durchgeführt. Als Ergebnis der Evaluation sollten Einsatzmöglichkeiten von SFX für die KOBV-Suchmaschine und in den lokalen Bibliothekssystemen und Informationsportalen aufgezeigt werden. Im Verlauf des Projektes hat sich das Produkt SFX als eine stabile Anwendung erwiesen, die dem Benutzer interessante zusätzliche Dienste bieten kann.

Description: In this work we present an approach for the sensitivity analysis of linearly-implicit differential-algebraic equation systems. Solutions for both, states and sensitivities are obtained by applying an extrapolated linearly implicit Euler discretization scheme. This approach is compared to the widely used sensitivity extensions of multi-step BDF methods by means of case studies. Especially, we point out the benefit of this method in the context of dynamic optimization using the sequential approach.

Description: Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol.

Description: The adaptive finite element code {\sc Kardos} solves nonlinear parabolic systems of partial differential equations. It is applied to a wide range of problems from physics, chemistry, and engineering in one, two, or three space dimensions. The implementation is based on the programming language C. Adaptive finite element techniques are employed to provide solvers of optimal complexity. This implies a posteriori error estimation, local mesh refinement, and preconditioning of linear systems. Linearely implicit time integrators of {\em Rosenbrock} type allow for controlling the time steps adaptively and for solving nonlinear problems without using {\em Newton's} iterations. The program has proved to be robust and reliable. The user's guide explains all details a user of {\sc Kardos} has to consider: the description of the partial differential equations with their boundary and initial conditions, the triangulation of the domain, and the setting of parameters controlling the numerical algorithm. A couple of examples makes familiar to problems which were treated with {\sc Kardos}. We are extending this guide continuously. The latest version is available by network: {\begin{rawhtml} 〈A href="http://www.zib.de/Numerik/software/kardos/"〉 〈i〉 Downloads.〈/i〉〈/a〉 \end{rawhtml}}

Description: This article studies the relation of the two scientific languages Chemistry and Mathematics via three selected comparisons: (a) QSSA versus dynamic ILDM in reaction kinetics, (b) lumping versus discrete Galerkin methods in polymer chemistry, and (c) geometrical conformations versus metastable conformations in drug design. The common clear message from these comparisons is that chemical intuition may pave the way for mathematical concepts just as chemical concepts may gain from mathematical precisioning. Along this line, significant improvements in chemical research and engineering have already been possible -- and can be further expected in the future from the dialogue between the two scientific languages.

Description: Several sets of reductions rules are known for preprocessing a graph when computing its treewidth. In this paper, we give reduction rules for a weighted variant of treewidth, motivated by the analysis of algorithms for probabilistic networks. We present two general reduction rules that are safe for weighted treewidth. They generalise many of the existing reduction rules for treewidth. Experimental results show that these reduction rules can significantly reduce the problem size for several instances of real-life probabilistic networks.

Description: Signaling is crucial to the operation of modern telecommunication networks. A breakdown in the signaling infrastructure typically causes customer service failures, incurs revenue losses, and hampers the company image. Therefore, the signaling network has to be highest reliability and survivability. This in particular holds for the routers in such a network, called \textit{signaling transfer points\/} (STPs). The robustness of an STP can be improved by equally distributing the load over the internal processing units. Several constraints have to be taken into account. The load of the links connected to a processing unit changes over time introducing an imbalance of the load. In this paper, we show how integer linear programming can be applied to reduce the imbalance within an STP, while keeping the number of changes small. Two alternative models are presented. Computational experiments validate the integer programming approach in practice. The GSM network operator E-Plus saves substantial amounts of time and money by employing the proposed approach.

Description: In the problem of \emph{Online Call Admission in Optical Networks}, briefly called \textsc{oca}, we are given a graph $G=(V,E)$ together with a set of wavelengths~$W$ and a finite sequence $\sigma=r_1,r_2,\dots$ of calls which arrive in an online fashion. Each call~$r_j$ specifies a pair of nodes to be connected and an integral demand indicating the number of required lightpaths. A lightpath is a path in~$G$ together with a wavelength~$\lambda \in W$. Upon arrival of a call, an online algorithm must decide immediately and irrevocably whether to accept or to reject the call without any knowledge of calls which appear later in the sequence. If the call is accepted, the algorithm must provide the requested number of lightpaths to connect the specified nodes. The essential restriction is the wavelength conflict constraint: each wavelength is available only once per edge, which implies that two lightpaths sharing an edge must have different wavelengths. Each accepted call contributes a benefit equal to its demand to the overall profit. The objective in \textsc{oca} is to maximize the overall profit. Competitive algorithms for \textsc{oca} have been known for the special case where every call requests just a single lightpath. In this paper we present the first competitive online algorithms for the general case of larger demands.

Description: Traditional optimization techniques assume, in general, knowledge of all data of a problem instance. There are many cases in practice, however, where decisions have to be made before complete information about the data is available. In fact, it may be necessary to produce a part of the problem solution as soon as a new piece of information becomes known. This is called an \emph{online situation}, and an algorithm is termed \emph{online}, if it makes a decision (computes a partial solution) whenever a new piece of data requests an action. \emph{Competitive analysis} has become a standard yardstick to measure the quality of online algorithms. One compares the solution produced by an online algorithm to that of an optimal (clairvoyant) offline algorithm. An online algorithm is called $c$-competitive if on every input the solution it produces has cost'' at most $c$~times that of the optimal offline algorithm. This situation can be imagined as a game between an online player and a malicious adversary. Although competitive analysis is a worst-case analysis and henceforth pessimistic, it often allows important insights into the problem structure. One can obtain an idea about what kind of strategies are promising for real-world systems and why. On the other hand there are also cases where the offline adversary is simply too powerful and allows only trivial competitiveness results. This phenomenon is called hitting the triviality barrier''. We investigate several online problems by means of competitive analysis. We also introduce new concepts to overcome the weaknesses of the standard approach and to go beyond the triviality barrier.

Description: The paper deals with the two-class priority M/M/1 system, where the prioritized class-1 customers are served under FCFS preemptive resume discipline and may become impatient during their waiting for service with generally distributed maximal waiting times but finite expectation. The class-2 customers have no impatience. The required mean service times may depend on the class of the customer. As the dynamics of class-1 customers are related to the well analyzed M/M/1+GI system, our aim is to derive characteristics for class-2 customers and for the whole system. The solution of the balance equations for the partial probability generating functions of the detailed system state process is given in terms of the weak solution of a family of boundary value problems for ordinary differential equations. By means of this solution formulae for the joint occupancy distribution and for the sojourn and waiting times of class-2 customers are derived generalizing results recently obtained by Choi et al. in case of deterministic maximal waiting times. For deterministic maximal waiting times partially new explicit formulae are given.

Description: The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the deduction of the Helmholtz term in the bio-heat transfer equation is not co role. In view of a future numerical application of this new mathematical model to treatment planning in hyperthermia we derive asymptotic estimates for first and second order correctors.

Description: Mixed integer programs ($MIPs$) are commonly solved with branch and bound algorithms based on linear programming. The success and the speed of the algorithm strongly depends on the strategy used to select the branching variables. Today's state-of-the-art strategy is called \emph{pseudocost branching} and uses information of previous branchings to determine the current branching. We propose a modification of \emph{pseudocost branching} which we call \emph{history branching}. This strategy has been implemented in $SIP$, a state-of-the-art $MIP$ solver. We give computational results that show the superiority of the new strategy.

Description: We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse wavelength conversion for efficient use of the capacities. In this paper, we investigate this extensive optical network design task. Using a flexible device-based model, we present an integer programming formulation that supports greenfield planning as well as expansion planning on top of an existing network. As solution method, we propose a suitable decomposition approach that separates the wavelength assignment from the dimensioning and routing. Our method in particular provides a lower bound on the total cost which allows to rate the solution quality. Computational experiments on realistic networks approve the solution approach to be appropriate.

Description: Today's telecommunication networks are configured statically. Whenever a connection is established, the customer has permanent access to it. However, it is observed that usually the connection is not used continuously. At this point, dynamic provisioning could increase the utilization of network resources. WDM based Optical Transport Networks (OTNs) will shortly allow for fast dynamic network reconfiguration. This enables optical broadband leased line services on demand. Since service requests competing for network resources may lead to service blocking, it is vital to use appropriate strategies for routing and wavelength assignment in transparent optical networks. We simulate the service blocking probabilities of various dynamic algorithms for this problem using a well-founded traffic model for two realistic networks. One of the algorithms using shortest path routings performs best on all instances. Surprisingly, the tie-breaking rule between equally short paths in different wavelengths decides between success or failure.

Description: Nachdem mit der KOBV-Suchmaschine die Online-Recherche in den wichtigsten Berliner und Brandenburgischen Bibliotheken realisiert ist, gehört der Aufbau der Online-Fernleihe als einer neuen, nutzerfreundlichen Dienstleistung zu den drängendsten Desideraten des KOBV. Dem Nutzer soll ein komfortabler Service geboten werden, der ihm im Anschluss an eine erfolgreiche Recherche die nahtlose - per Knopfdruck ausgelöste - Fernleih-Bestellung auf das gewünschte Medium erlaubt. Gleichzeitig trägt die Ablösung des traditionellen, per Post und Bücherauto versandten Roten Fernleihscheines durch eine sekundenschnelle Online-Kommunikation zu einer erheblichen Beschleunigung des Fernleih-Verfahrens bei. Der KOBV beteiligt sich an der Initiative der deutschen Bibliotheksverbünde zur Automatisierung und Beschleunigung der Fernleihe. Die Realisierung soll im KOBV in einem zweistufigen Verfahren erfolgen: (1) verbundinterne Fernleihe im KOBV und (2) verbundübergreifende Fernleihe in der Zusammenarbeit mit den anderen Verbünden. Eine Verbund-Fernleih-Software für den KOBV muss insbesondere den KOBV-spezifischen Gegebenheiten genügen, die in dieser Form in den anderen deutschen Verbünden nicht anzutreffen sind. Im Jahre 2001 hat eine KOBV-Arbeitsgruppe Spezifikationen für eine Verbund-Fernleih-Software erarbeitet, in der die Besonderheiten des KOBV mit berücksichtigt sind. Beim Aufbau der automatisierten Fernleihe als einer regulären KOBV-Dienstleistung geht es nicht allein darum, einen schnellen, komfortablen Service für Nutzer einzurichten, sondern darüber hinaus um eine weitreichende Rationalisierung innerhalb der Bibliotheken. Das vorliegende Spezifikationspapier zielt auf beide Faktoren ab, indem es die Fernleihe als integrierten Dienst entwirft, der von der Bestellung bis zur Bereitstellung des Mediums in der gebenden Bibliothek automatisiert - ohne manuelles Eingreifen der Fernleihstelle - abläuft: die jetzige manuell durchgeführte Fernleihe wird durch die automatisierte Fernleihe abgelöst.

Description: In the online traveling salesman problem $OLTSP$ requests for visits to cities arrive online while the salesman is traveling. We study the $F{\_max}-OLTSP$ where the objective is to minimize the maximum flow time. This objective is particularly interesting for applications. Unfortunately, there can be no competitive algorithm, neither deterministic nor randomized. Hence, competitive analysis fails to distinguish online algorithms. Not even resource augmentation which is helpful in scheduling works as a remedy. This unsatisfactory situation motivates the search for alternative analysis methods. We introduce a natural restriction on the adversary for the $F{\_max}-OLTSP$ on the real line. A \emph{non-abusive adversary} may only move in a direction if there are yet unserved requests on this side. Our main result is an algorithm which achieves a constant competitive ratio against the non-abusive adversary.

Description: While attribute-value pairs are a popular method to name objects, information retrieval from those attribute-based namespaces is not an easy task. The user has to recall correct attribute names and values and master the syntax and semantics of query formulation. This paper describes hierarchical structures in attribute-based namespaces, shows how to extract them efficiently and evaluates the quality of these structures in an user experiment. It proposes an user interface for browsing attribute-named object sets which makes this task resemble todays file-system browsers and compares the usability of this interface to normal form-based methods in an user study.

Description: In this paper, we quantify and discuss the physical and surface chemical processes leading to the formation, temporal evolution and sedimentation of dust grains in brown dwarf and giant gas planet atmospheres: nucleation, growth, evaporation and gravitational settling. Considering dust particles of arbitrary sizes in the different hydrodynamical regimes (free molecular flow, laminar flow, turbulent flow), we evaluate the equilibrium drift velocities (final fall speeds) and the growth rates of the particles due to accretion of molecules. We show that a depth-dependent maximum size of the order of $a_{\rm max}\!\approx\!1\,\mu{\rm m\,(upper\ regions)} \ldots 100\,\mu{\rm m\,(lower\ regions)}$ exists, which depends on the condensate and the stellar parameters, beyond which gravitational settling is faster than growth. Larger particles can probably not be formed and sustained in brown dwarf atmospheres. We furthermore argue that the acceleration towards equilibrium drift is always very fast and that the temperature increase of the grains due to the release of latent heat during the growth process is negligible. Based on these findings, we formulate the problem of dust formation coupled to the local element depletion/enrichment of the gas in brown dwarf atmospheres by means of a system of partial differential equations. These equations state an extension of the moment method developed by Gail\plus Sedlmayr\,(1988) with an additional advective term to account for the effect of size-dependent drift velocities of the grains. A dimensionless analysis of the new equations reveals a hierarchy of nucleation $\to$ growth $\to$ drift $\to$ evaporation, which characterises the life cycle of dust grains in brown dwarf atmospheres. The developed moment equations can be included into hydrodynamics or classical stellar atmosphere models. Applications of this description will be presented in a forthcoming paper of this series.

Description: Global grid environments do not only provide massive aggregated computing power but also an unprecedented amount of distributed storage space. Unfortunately, dynamic changes caused by component failures, local decisions, and irregular data updates make it difficult to efficiently use this capacity. In this paper, we address the problem of improving data availability in the presence of unreliable components. We present an analytical model for determining an optimal combination of distributed replica catalogs, catalog sizes, and replica servers. Empirical simulation results confirm the accuracy of our theoretical analysis. Our model captures the characteristics of highly dynamic environments like peer-to-peer networks, but it can also be applied to more centralized, less dynamic grid environments like the European {\em DataGrid}.

Description: Das Management von großen Datenmengen spielt eine immer wichtigere Rolle, wie aktuelle Entwicklungen in der Hochenergiephysik [2] zeigen. Für das DataGrid-Projekt zum Beispiel ist es notwendig, große Datenmengen auf mehrere Rechenzentren in Europa zu verteilen und die Daten untereinander zu synchronisieren. Auch innerhalb von Clustern gewinnen mit zunehmender Anzahl der Knoten Werkzeuge zur effizienten Synchronisation und Verteilung von Daten an Bedeutung. Im Rahmen dieser Arbeit wurde ein effizientes Verfahren zur Synchronisation von verteilten Verzeichnisstrukturen entwickelt und implementiert. Mit diesem Verfahren ist es möglich, unabhängige Änderungen an beliebigen Repositories gleichzeitig durchzuführen. Das Verfahren benötigt keine zentrale Instanz, wodurch eine gegenüber vielen existierenden Verfahren verbesserte Skalierbarkeit erreicht werden konnte. Dabei wurden Erkenntnisse aus der Graphentheorie eingesetzt und weiterentwickelt, um die Netzwerktopolo-gie und -handbreiten zwischen den Rechnern zu berücksichtigen. Durch die Verwendung einer Offline-Synchronisation werden Änderungen erst dann an andere Rechner propagiert, wenn der Nutzer dies anstößt. Das kann zum Beispiel nach einer abgeschlossenen Transaktion, die Änderungen an mehreren Dateien beinhaltet, angemessen sein.

Description: Current developments in high energy physics [2] show that the management of large datasets plays an important role. For the DataGrid project it is necessary to distribute large datasets over several computing centers all over Europe and to synchronize these datasets. Within clusters tools for efficient synchronization and distribution of data become more important, too. In this thesis, a method to synchronize distributed directory structures was developed and implemented which makes it possible to perform independent changes to arbitrary repositories simultaneously. This method needs no central instance and therefore the presented system achieves a better scalability than many existing systems. Knowledge from graph theory was used and improved to take the network topology and the network bandwidth between the computers into account. By using offline synchronization, changes will only be propagated when the user initiates it. This can be reasonable after a completed transaction which consists of changes on several files.

Description: An instance of the \emph{maximum coverage} problem is given by a set of weighted ground elements and a cost weighted family of subsets of the ground element set. The goal is to select a subfamily of total cost of at most that of a given budget maximizing the weight of the covered elements. We formulate the problem on graphs: In this situation the set of ground elements is specified by the nodes of a graph, while the family of covering sets is restricted to connected subgraphs. We show that on general graphs the problem is polynomial time solvable if restricted to sets of size at most~$2$, but becomes NP-hard if sets of size~$3$ are permitted. On trees, we prove polynomial time solvability if each node appears in a fixed number of sets. In contrast, if vertices are allowed to appear an unbounded number of times, the problem is NP-hard even on stars. We finally give polynomial time algorithms for special cases where the subgraphs form paths and the host graph is a line, a cycle or a star.

Description: Hinter der für den Uneingeweihten etwas kryptischen Frage "P = NP?" verbirgt sich das derzeit wichtigste Problem der Komplexitätstheorie. Dieser Artikel erläutert einige Aspekte der Theorie und erklärt informell, was "P = NP?" bedeutet. Es geht nicht nur um komplizierte algorithmische Mathematik und Informatik, sondern um grundsätzliche Fragen unserer Lebensumwelt. Kann man vielleicht beweisen, dass es für viele Probleme unseres Alltags keine effizienten Lösungsmethoden gibt?

Description: The Cooperative Library Network Berlin-Brandenburg (KOBV) has set the development of a genuine library information portal for the two German Lander (federal states) Berlin and Brandenburg as its main task for the next years. This joined effort is driven by the vision of an user friendly Internet information portal which is accessible anytime, from anywhere in the world. The idea of a regional information portal can be understood as the logically consistent development of the basic ideas of the KOBV. Starting in 1997, the consortia has set the implementation of a virtual OPAC instead of a physical union catalogue as its goal. The result was the KOBV-Search Engine which already has some qualities of a portal itself. The paper begins with initial remarks about the German library world, which do form the background for the project and its initiator - the KOBV consortia. After this preliminary part, different types of portals are introduced. The basic features of the KOBV-Search Engine as one of the cornerstones of the future portal are discussed in the following. The information portal will be much richer in content and services for the end-user. Two aspects are focused on in more detail: the presentation of resources, which becomes a compelling requirement because of the broader range of content and the personalization of services, as one important feature to suit user's individual needs.

Description: The paper presents a particle method framework for resolving molecular dynamics. Error estimators for both the temporal and spatial discretization are advocated and facilitate a fully adaptive propagation. For time integration, the implicit trapezoidal rule is employed, where an explicit predictor enables large time steps. The framework is developed and exemplified in the context of the classical Liouville equation, where Gaussian phase-space packets are used as particles. Simplified variants are discussed shortly, which should prove to be easily implementable in common molecular dynamics codes. A concept is illustrated by numerical examples for one-dimensional dynamics in double well potential.

Description: The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and inexact Newton methods, where an inner iteration is used instead, are synoptically presented, both in affine invariant convergence theory and in numerical experiments. The three types of algorithms are: (a) affine covariant (formerly just called affine invariant) Newton algorithms, oriented toward the iterative errors, (b) affine contravariant Newton algorithms, based on iterative residual norms, and (c) affine conjugate Newton algorithms for convex optimization problems and discrete nonlinear elliptic PDEs.

Description: In Analogie zu den Elektrizitätsnetzen electricity grid), von denen die technische Revolution ausging, wurde der Begriff Computational Grid (kurz Grid) geprägt. Ein wichtiger Bestandteil des Systems liegt im benutzerfreundlichen Zugang und der koordinierten Nutzung der weltweit verteilten Speicherressourcen und Rechnerkapazitäten. Bei der Entwicklung dazu notwendiger Technologien und Software (Middleware) profitiert man von Kenntnissen und Erfahrungen bei der Entwicklung verteilter Algorithmen, dem Software-Engineering und dem Supercomputing.

Description: In this article we study the problem of designing a nation-wide communication network. Such networks usually consist of an access layer, a backbone layer, and maybe several intermediate layers. The nodes of each layer must be connected to those of the next layer in a tree-like fashion. The backbone layer has to satisfy certain survivability and routing constraints. Given the node locations, the demands between them, the possible connections and hardware configurations, and various other technical and administrational constraints, the goal is to decide, which node is assigned to which network level, how the nodes are connected, what hardware must be installed, and how traffic is routed in the backbone. Mixed integer linear programming models and solution methods are presented for both the access and the backbone network design problem. The focus is on the design of IP-over-SDH networks, but the access network design model and large parts of the backbone network design models are general and also applicable for other types of communication networks. Results obtained with these methods in the planning of the German research network are presented.

Description: We present an online algorithm for a real-world vehicle dispatching problem at ADAC, the German Automobile Association.

Description: Eine fremddatengestützte Katalogisierung bedeutet für die einzelne Bibliothek unbestritten eine Zeit- und Kostenersparnis. Dieser Report beleuchtet die unterschiedlichen Faktoren technischer und organisatorischer Natur, die die Fremddatennutzung in der dezentralen Struktur des Kooperativen Bibliotheksverbundes Berlin-Brandenburg (KOBV) beeinflussen. Die Ausführungen stützen sich im Wesentlichen auf eine Umfrage, die die Autoren im Mai / Juni 2002 unter KOBV-Mitgliedsbibliotheken zum Thema Fremddatennutzung durchgeführt haben. Dargelegt wird, wie komfortabel die in den KOBV-Bibliotheken eingesetzten Bibliotheksinformationssysteme eine fremddatengestützte Katalogisierung erlauben. Diskutiert wird zudem die Software ZACK, die sich als Alternative zu einem eigenen Z39.50-Client zur Datenübernahme anbietet. Erstmals seit Bestehen des Verbundes werden Zahlen veröffentlicht über den Anteil der Bibliotheken, die Fremddaten nutzen und denjenigen, die dieses Angebot nicht wahrnehmen. Dabei wird die Fremddatenutzung differenziert sowohl für den Bereich der Neuaufnahmen als auch für die Retrokatalogisierung. In der weiteren Analyse werden zusätzliche Aspekte betrachtet wie z.B. die verfügbaren bzw. gewünschten Datenbanken im Verhältnis zum sprachlichen Spektrum des erworbenen Katalogisierungsgutes. Eingegangen wird auch auf die von den Bibliotheken genannten Hauptproblemen und die gewünschten zusätzlichen Serviceleistungen auf Seiten der KOBV-Verbundzentrale. Als Ergebnis dieses Status-Quo-Berichts legt das Autorenteam eine Reihe von Empfehlungen vor, die darauf abzielen, auch für KOBV-Bibliotheken in Zukunft eine Fremddatennutzungsquote von 70 - 75 % zu erreichen.

Description: Substellar atmospheres are cool and dense enough that dust forms very efficiently. As soon as these particles are formed, they sizedependently precipitate due to the large gravity of the objects. Arriving in hot atmospheric layers, the dust evaporates and enriches the gas by those elements from which it has formed. The upper atmospheric layers are depleted by the same elements. Non-continuous and spatially inhomogeneous convective element replenishment, generating a turbulent fluid field, completes the circuit of dust. The formation of dust in substellar atmosphere is described by extending the classical theory of Gail\plus Sedlmayr for the case of different gas and dust velocities. Turbulence is modeled in different scale regimes which reveals turbulence as trigger for dust formation in hot environments. Both mechanisms cause the dust to be present in else wise dust-hostile region: precipitation transports the dust into hot regions, and turbulence allows the formation of dust in there.

Description: The talk given by the author at the CRM workshop on Superintegrability in Sep.\ 2002 and this related paper report on work in two subjects. One is the collaboration with Vladimir Sokolov and Takayuki Tsuchida in an effort to classify polynomial integrable vector evolution equations. The other is the computer algebra package {\sc Crack} which did the main computations in solving large bi-linear algebraic systems. Although originally designed to solve over-determined systems of partial differential equations a number of extensions made {\sc Crack} a powerful tool for solving systems of bi-linear algebraic equations. Such systems turn up in many different classification problems some of which were investigated by other participants of this workshop. Two additional applications are outlined. In the talk on which this article is based a method to reduce the length of equations was presented which proved to be useful in solving the bi-linear algebraic systems. Due to numerous asked questions about the computer program, a more complete overview is given in the appendix.

Description: Die KOBV-Suchmaschine hat seit ihrer Inbetriebnahme Ende 1999 entscheidend zur Verbesserung der Informationsinfrastruktur in Berlin und Brandenburg beigetragen. Auf der Basis der offenen Plattform KOBV-Suchmaschine wird die KOBV-Zentrale gemeinsam mit den Bibliotheken in den nächsten Jahren das Dienstleistungsangebot des KOBV und seiner Bibliotheken kontinuierlich erweitern. Dabei sollen die Prinzipien des KOBV - Offenheit, Heterogenität und Dezentralität auf technischer und organisatorischer Ebene - gewahrt bleiben. Die einzelnen KOBV-Bibliotheken werden sich mit ihren Angeboten in unterschiedlicher Weise im Web positionieren. Die Integration auf regionaler Ebene kann und soll die lokalen Angebote nicht künstlich vereinheitlichen. Das kooperative Portal, das in der Region aufgebaut wird, ist als System geplant, in dem zentrales Portal und lokale Portale nicht hierarchisch einander zugeordnet, sondern miteinander vernetzt sind. Das \glqq KOBV-Informationsportal \grqq soll in der KOBV-Zentrale im Rahmen eines wissenschaftlichen Projektes von Mitte 2001 bis Ende 2003 aufgebaut werden. Das vorliegende Papier gibt einen ersten allgemeinen Einblick, welche Funktionen das \glqq KOBV-Informationsporta \grqq umfassen soll und stellt die Teilprojekte der 1. Stufe vor.

Description: Oriented matroids are combinatorial structures that encode the combinatorics of point configurations. The set of all triangulations of a point configuration depends only on its oriented matroid. We survey the most important ingredients necessary to exploit oriented matroids as a data structure for computing all triangulations of a point configuration, and report on experience with an implementation of these concepts in the software package TOPCOM. Next, we briefly overview the construction and an application of the secondary polytope of a point configuration, and calculate some examples illustrating how our tools were integrated into the {\sc polymake} framework.

Description: For all perfect graphs, the stable set polytope STAB$(G)$ coincides with the fractional stable set polytope QSTAB$(G)$, whereas STAB$(G) \subset$ QSTAB$(G)$ holds iff $G$ is imperfect. Padberg asked in the early seventies for ``almost'' perfect graphs. He characterized those graphs for which the difference between STAB$(G)$ and QSTAB$(G)$ is smallest possible. We develop this idea further and define three polytopes between STAB$(G)$ and QSTAB$(G)$ by allowing certain sets of cutting planes only to cut off all the fractional vertices of QSTAB$(G)$. The difference between QSTAB$(G)$ and the largest of the three polytopes coinciding with STAB$(G)$ gives some information on the stage of imperfectness of the graph~$G$. We obtain a nested collection of three superclasses of perfect graphs and survey which graphs are known to belong to one of those three superclasses. This answers the question: which graphs are ``almost'' perfect?

Description: Die Automatisierung von innerbetrieblicher Logistik erfordert -- über die physikalische Steuerung von Geräten hinaus -- auch eine effiziente Organisation der Transporte: ein Aufgabenfeld der kombinatorischen Optimierung. Dieser Artikel illustriert anhand von konkreten Aufgabenstellungen die Online-Problematik (unvollständiges Wissen) sowie die Echtzeit-Problematik (beschränkte Rechenzeit), auf die man in der innerbetrieblichen Logistik trifft. Der Text gibt einen Überblick über allgemeine Konstruktionsprinzipien für Online-Algorithmen und Bewertungsmethoden, die bei der Entscheidung helfen, welche Algorithmen für eine vorliegende Problemstellung geeignet sind.

Description: \We discuss a nested collection of three superclasses of perfect graphs: near-perfect, rank-perfect, and weakly rank-perfect graphs. For that, we start with the description of the stable set polytope for perfect graphs and allow stepwise more general facets for the stable set polytopes of the graphs in each superclass. Membership in those three classes indicates how far a graph is away from being perfect. We investigate for webs and antiwebs to which of the three classes they belong. We provide a complete description of the facets of the stable set polytope for antiwebs (with help of a result due to Shepherd on near-bipartite graphs). The main result is that antiwebs are rankperfect.

Description: \textsf{\itshape{GuiGen}} is a comprehensive set of tools for creating customized graphical user interfaces (GUIs). It draws from the concept of computing portals, which are here seen as interfaces to application-specific computing services for user communities. While \textsf{\itshape{GuiGen}} was originally designed for the use in computational grids, it can be used in client/server environments as well. Compared to other GUI generators, \textsf{\itshape{GuiGen}} is more versatile and more portable. It can be employed in many different application domains and on different target platforms. With \textsf{\itshape{GuiGen}}, application experts (rather than computer scientists) are able to create their own individually tailored GUIs.

Description: The purpose of the paper is to formulate and use syzygies for systems of linear PDEs. The computation of an equivalent of a GCD for linear partial differential operators will save us their factorization which is otherwise only possible algorithmically in special cases. After showing the computation with the new and the traditional method and comparing both in the next three sections, the algorithm is explained in general and an overview is given.

Description: Telekommunikation ist seit Jahren \glqq in\grqq. Zunächst gab es einen enormen Aufschwung; neue Technologien und Dienste haben eine überwältigende, nicht vorhersehbare Akzeptanz gefunden. Derzeit ist -- ausgelöst durch die UMTS-Lizenzversteigerungen, Rezessions- und Sättigungstendenzen -- eine Krise zu verzeichnen. Viele (auch wir) sind davon überzeugt, dass technischer Fortschritt und nützliche Dienste demnächst die Stimmung wieder ändern werden. Wenigen ist allerdings bewusst, welche Rolle Mathematik bei der Entwicklung und dem effizienten Einsatz vieler der neuen Kommunikationstechnologien spielt. In diesem Artikel soll kein Überblick über diesen umfangreichen Themenkreis gegeben werden. Wir zeigen lediglich an einem konkreten Beispiel aus dem Mobilfunk, der Frequenzplanung in GSM-Funknetzen, was man durch geeignete Modellierung der praktischen Fragestellung und den Einsatz problemadäquater Algorithmen erreichen kann.

Description: Wir beschreiben einen Ansatz zur integrierten Umlauf- und Dienstplanung im öffentlichen Nahverkehr. Der Ansatz zielt auf die Verbesserung des Gesamtwirkungsgrades dieser beiden Planungsschritte und auf die besondere Planungsproblematik im Regionalverkehr. Wir entwickeln dazu mathematische Optimierungstechniken für den Einsatz in den Planungssystemen MICROBUS II und DIVA.

Description: A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case $n\choose 2$ entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity (Best et al) or $k$-colorability (Bollobas). A famous conjecture of Karp says that every non-trivial monotone graph property is elusive. We prove that a non-monotone but hereditary graph property is elusive: perfectness.

Description: Recently, a novel approach for the analysis of molecular dynamics on the basis of a transfer operator has been introduced. Therein conformations are considered to be disjoint metastable clusters within position space of a molecule. These clusters are defined by almost invariant characteristic functions that can be computed via {\em Perron Cluster} analysis. The present paper suggests to replace crisp clusters with {\em fuzzy} clusters, i.e. to replace characteristic functions with membership functions. This allows a more sufficient characterization of transiton states between different confor conformations and therefore leads to a better understanding of molecular dynamics. Fur thermore, an indicator for the uniqueness of metastable fuzzy clusters and a fast algorithm for the computation of these clusters are described. Numerical examples are included.

Description: The paper provides a detailed analysis of a short step interior point algorithm applied to linear control constrained optimal control problems. Using an affine invariant local norm and an inexact Newton corrector, the well-known convergence results from finite dimensional linear programming can be extended to the infinite dimensional setting of optimal control. The present work complements a recent paper of Weiser and Deuflhard, where convergence rates have not been derived. The choice of free parameters, i.e. the corrector accuracy and the number of corrector steps, is discussed.

Description: Pseudo--transient continuation methods are quite popular for the numerical solution of steady state problems, typically in PDEs. They are based on an embedding into a time dependent initial value problem. In the presence of dynamical invariants the Jacobian matrix of the nonlinear equation system is bound to be singular. The paper presents a convergence analysis which takes this property into account -- in contrast to known approaches. On the basis of the new analysis adaptive algorithms are suggested in detail. These include a variant with Jacobian approximations as well as inexact pseudo--transient continuation, both of which play an important role in discretized PDEs. Numerical experiments are left to future work.

Description: A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every $d$-dimensional polyhedron admits a representation as the set of solutions of at most $d(d+1)/2$ polynomial inequalities. Even in this polyhedral case, however, no constructive proof is known, even if the quadratic upper bound is replaced by any bound depending only on the dimension. Here we give, for simple polytopes, an explicit construction of polynomials describing such a polytope. The number of used polynomials is exponential in the dimension, but in the 2- and 3-dimensional case we get the expected number $d(d+1)/2$.

Description: TOPCOM is a package for computing triangulations of point configurations and oriented matroids. For example, for a point configuration one can compute the chirotope, components of the flip graph of triangulations, enumerate all triangulations. The core algorithms implemented in TOPCOM are described, and implentation issues are discussed.

Description: A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixed-integer variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up- and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) hand-over. It is also explained how to use the model as a basis for rating network configurations.

Description: Computational drug design studies molecular recognition in the {\em virtual lab}. The arising Hamiltonian dynamics is known to be chaotic and ill-conditioned already after picoseconds, whereas times are $msec$ up to $min$. Classical molecular dynamics with long term trajectory computation gives, at best, information about time and statistical ensemble averages. The present paper surveys a recent new modeling approach called {\em conformational dynamics}, which is due to the author and Ch. Schütte. This approach achieves information about the dy time scales by telescoping a short term deterministic model with a statistical model. Examples of small biomolecules are included.

Description: Combinatorial online optimization is an area with lots of applications and potential for significant progress, both in theory and practice. In this short note we sketch the ADACproblem, a typical large-scale online optimization problem, discuss some theoretical and pratical issues coming up, and explain, very briefly, how we approach this problem mathematically. Online problems are a battlefield of heuristics with many strong claims about their solution quality. We indicate that a stronger problem orientation and the use of a little more mathematics may yield.

Description: A subset ${\cal C}$ of the power set of a finite set $E$ is called cardinality homogeneous if, whenever ${\cal C}$ contains some set $F$, ${\cal C}$ contains all subsets of $E$ of cardinality $|F|$. Examples of such set systems ${\cal C}$ are the sets of circuits and the sets of cycles of uniform matroids and the sets of all even or of all odd cardinality subsets of $E$. With each cardinality homogeneous set system ${\cal C}$, we associate the polytope $P({\cal C})$, the convex hull of the incidence vectors of all sets in ${\cal C}$, and provide a complete and nonredundant linear description of $P({\cal C})$. We show that a greedy algorithm optimizes any linear function over $P({\cal C})$, give an explicit optimum solution of the dual linear program, and provide a polynomial time separation algorithm for the class of polytopes of type $P({\cal C})$.

Description: Die Bibliotheken des KOBV haben im Jahr 2001 die Entwicklung der KOBV-Suchmaschine zu einem gemeinsamen Informationsportal Berlin-Brandenburg und den Aufbau lokaler Bibliotheksportale als Hauptentwicklungsziele des KOBV definiert. Diese Informationsportale sollen mit Standardsoftware realisiert werden. Um die Auswahl eines Systems zu unterstützen, wurde in der Zentrale des KOBV ausgewählte Systeme untersucht. In der Arbeit werden zahlreiche Kriterien vorgestellt, auf Grund derer die betreffenden Systeme beurteilt werden. Die Kriterien umfassen sowohl Aspekte aus der Sicht der Benutzer als auch Kriterien aus der Sicht der Betreiber eines solchen Systems. Wesentliche Funktionen und die Realisierung von verschiedenen Merkmalen werden im Bericht ausführlich beschrieben. Daneben liefert eine Tabelle mit allen betrachteten Kriterien eine Übersicht über vorhandene Merkmale und der Art der Realisierung.

Description: In the cake cutting problem, $n\ge2$ players want to cut a cake into $n$ pieces so that every player gets a ``fair'' share of the cake by his own measure. We describe a protocol with $n-1$~cuts in which each player can enforce to get a share of at least~$1/(2n-2)$. Moreover we show that no protocol with $n-1$~cuts can guarantee a better fraction.

Description: We present a new efficient algorithm for the solution of direct time-harmonic scattering problems based on the Laplace transform. This method does not rely on an explicit knowledge of a Green function or a series representation of the solution, and it can be used for the solution of problems with radially symmetric potentials and problems with waveguides. The starting point is an alternative characterization of outgoing waves called \emph{pole condition}, which is equivalent to Sommerfeld's radiation condition for problems with radially symmetric potentials. We obtain a new representation formula, which can be used for a numerical evaluation of the exterior field in a postprocessing step. Based on previous theoretical studies, we discuss the numerical realization of our algorithm and compare its performance to the PML method.

Description: The aim of this paper is to develop fast methods for the solution of nonlinear Schrödinger type equations in fiber optics. Using the method of lines we have to solve a stiff system of ordinary differential equations where the eigenvalues of the Jacobian are close to the imaginary axis. This is usually done by a Split Step method. Here we consider the extrapolation of Split Step methods with adaptive order and step size control. For more complicated nonlinearities, in particular stimulated Raman scattering, Split Step methods are less efficient since symmetry is either destroyed or requires much additional effort. In this case we use implicit Runge Kutta formulas of Gauß type. The key point for the efficient implementation of these methods is that the system of nonlinear algebraic equations can be solved without setting up the Jacobian. The proposed methods are compared to other methods, in particular exponential integrators, the method of Marcuse, and the method of Blow and Wood.

Description: The work presents a new approach to the numerical solution of time-harmonic and time-dependent scattering problems. We replace Sommerfeld's radiation condition valid for the Helmholtz equation by a more general concept called pole condition. The pole condition is based on the Laplace transform of the exterior solution and allows a characterization of outgoing waves. Both new insight into the analysis of scattering problems as well as new numerical algorithms are obtained.

Description: An edge of a perfect graph $G$ is critical if $G-e$ is imperfect. We would like to decide whether $G - e$ is still {\sl almost perfect} or already {\sl very imperfect}. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.

Description: Collection of abstracts of the first SIAM-EMS conference Applied Mathematics in our Changing World'' in Berlin, September 2-6, 2001.

Description: {\sc Zimpl} is a little language to translate the mathematical model of a problem into a linear or (mixed-)integer mathematical program expressed in {\tt lp} or {\tt mps} file format which can be read by a LP or MIP solver.

Description: Im ersten Teil des folgenden Aufsatzes werden allgemeine Überlegungen zur Entwicklung von Bibliotheken hin zu Informationsvermittlungsstellen für sowohl elektronische wie auch gedruckte Medien angestellt. Basierend auf den Ergebnissen der Evaluation digitaler Bibliotheken und Informationsportale in Deutschland wird ein erster Kriterienkatalog für ein Verbund-Informationsportal für den Kooperativen Bibliotheksverbund Berlin-Brandenburg entwickelt. Im Anhang befindet sich der Statusbericht über Informationsportale und digitale Bibliotheken in Deutschland. Dazu wurden sieben digitale Bibliotheken auf Verbundebene und 21 Bibliotheken nach Bundesländern evaluiert.

Description: Given a set of service requests (events), a set of guided servers (units), and a set of unguided service contractors (conts), the vehicle dispatching problem {\sl vdp} is the task to find an assignment of events to units and conts as well as tours for all units starting at their current positions and ending at their home positions (dispatch) such that the total cost of the dispatch is minimized. The cost of a dispatch is the sum of unit costs, cont costs, and event costs. Unit costs consist of driving costs, service costs and overtime costs; cont costs consist of a fixed cost per service; event costs consist of late costs linear in the late time, which occur whenever the service of the event starts later than its deadline. The program \textsf{ZIBDIP} based on dynamic column generation and set partitioning yields solutions on heavy-load real-world instances (215 events, 95 units) in less than a minute that are no worse than 1\% from optimum on state-of-the-art personal computers.

Description: Scenario tree models of stochastic programs arise naturally under standard nonanticipativity assumptions. We demonstrate how tree-sparse programs cover the general case, with \emph{arbitrary} information constraints. Detailed examples and intuitive interpretations illuminate the basic thoughts behind the abstract but elementary construction.

Description: In this paper we present an algorithm that accelerates 3D texture-based volume rendering of large and sparse data sets. A hierarchical data structure (known as AMR tree) consisting of nested uniform grids is employed in order to efficiently encode regions of interest. The hierarchies resulting from this kind of space partitioning yield a good balance between the amount of volume to render and the number of texture bricks -- a prerequisite for fast rendering. Comparing our approach to an octree based algorithm we show that our algorithm increases rendering performance significantly for sparse data. A further advantage is that less parameter tuning is necessary.

Description: Mathematical optimization techniques are on their way to becoming a standard tool in chemical process engineering. While such approaches are usually based on deterministic models, uncertainties such as external disturbances play a significant role in many real-life applications. The present article gives an introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization.

Description: Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the $n$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.

Description: Standard model predictive control for real-time operation of industrial production processes may be inefficient in the presence of substantial uncertainties. To avoid overly conservative disturbance corrections while ensuring safe operation, random influences should be taken into account explicitly. We propose a multistage stochastic programming approach within the model predictive control framework and apply it to a distillation process with a feed tank buffering external sources. A preliminary comparison to a probabilistic constraints approach is given and first computational results for the distillation process are presented.

Description: Dynamic stochastic programs are prototypical for optimization problems with an inherent tree structure inducing characteristic sparsity patterns in the KKT systems of interior methods. We propose an integrated modeling and solution approach for such tree-sparse programs. Three closely related natural formulations are theoretically analyzed from a control-theoretic viewpoint and compared to each other. Associated KKT solution algorithms with linear complexity are developed and comparisons to other interior approaches and related problem formulations are discussed.

Description: We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly enviroment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size~$B\in\mathbb{N}$. The packing process is subject to the constraint that at any moment in time at most $q\in\mathbb{N}$ bins may be partially filled. Moreover, bins may only be closed if they are filled completely. An online algorithm must pack each item must be packed without knowledge of any future items. We investigate the existence of competitive online algorithms for the online uniform binpacking problem. We show upper bounds for the bin coloring problem. We prove an upper bound of $3q$ - 1 and a lower bound of $2q$ for the competitive ratio of a natural greedy-type algorithm, and show that surprisingly a trivial algorithm which uses only one open bin has a strictly better competitive ratio of $2q$ - 1. Morever, we show that any deterministic algorithm has a competitive ratio $\Omega (q)$ and that randomization does not improve this lower bound even when the adversary is oblivious.

Description: In circuit switching networks call streams are characterized by their mean and peakedness (two-moment method). The $GI/M/C/0$ system is used to model a single link, where the $GI$-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a $GI/M/C/0$ system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d.\ holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used rigorously. The main result of this paper is an efficient algorithm for computing the moments of the freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.

Description: In this work we concentrate on developing methods which determine good lower bounds for set partitioning problems (SPP) in an appropriate amount of time. We found out that it makes sense to use the Lagrangian relaxation method for this task. The Lagrangian relaxed problem of SPP has a simple structure, which leads to algorithms and heuristics, whose total complexity per iteration depends linearly on the number of non-zeros of the problem matrix of SPP. In contrast, other methods like simplex methods or interior point methods have a complexity of higher order. Because the problem matrices of our tested instances are sparse, the linear dependence becomes an advantage for the algorithms and heuristics mentioned above. As a reference for the state-of-the-art we have applied the dual simplex method and the barrier function method, implemented in CPLEX. The methods, which we have developed and compared with those of CPLEX, are SBM, CAM, CCBM, and CBM. SBM is a subgradient bundle method derived from the basic subgradient method, which is a global convergent method for determining the maximum of concave functions. CAM is a coordinate ascent method, where the convex coordinate bundle method CCBM and the coordinate bundle method CBM are derivatives from CAM. We observed that the basic subgradient and the coordinate ascent method are improved if bundling techniques can be used. But the motivation for bundling differs for both approaches. In the former case bundling helps to approximate a minimum norm subgradient, which provides a steepest ascent direction, in order to speed up the performance. In the latter case bundling enables proceeding along directions, which are not restricted on the coordinate directions. By this the performance is accelerated. Among all used techniques stabilization is worth mentioning. Stabilization improves the performance especially at the beginning by avoiding too big steps during the proceeding. This leads to a more stabilized progression. Stabilization was successfully applied to SBM, CAM, CCBM, and CBM. As an overall result we conclude the following: \begin{enumerate} \item CPLEX computes the optimal objective values, whereas SBM and CBM has on average a gap of under $1.5\%$. \item In comparison to CPLEX baropt, SBM, CAM, and CBM the algorithm CCBM has a slow convergence because of the convex combination of ascent coordinate directions. An alternative is to relax the convex combination to a simple sum of the corresponding directions. This idea is realized in CBM. \item If we focus on the running time rather than on optimality then CBM is on average the fastest algorithm. \end{enumerate} Note that methods like SBM or CBM are applied on static SPP instances in order to determine a good lower bound. For solving SPP we need dynamical methods. Due to the complex topic of dynamical methods we will not discuss them, but a certain technique is worth mentioning. It is called column generation. We have indicated that this technique needs good Lagrangian multipliers of the corresponding SPP instances in order to generate further columns (in our case duties), which are added to the current SPP instance. Those multipliers are by-products of methods like our six considered methods. Due to the large number of such generation steps the running time depends on the computation time of these methods. Therefore, CBM fits more to this technique than CPLEX baropt or SBM. To sum it up it can be said that applications such as a duty scheduling can be described as set partitioning problems, whose lower bound can be solved by simplex, interior points, subgradient, or coordinate ascent methods. It turns out that the interior points method CPLEX baropt and the heuristic CBM have good performances. Furthermore, good Lagrangian multipliers, which are by-products of these methods, can be used by techniques like column generation. For this particular technique it also turns out that among our tested algorithms CBM is the most efficient one. In general we can state that real-world applications, which have to solve a large number of Lagrangian relaxed SPP instances can improve their performance by using CBM.

Description: The success of large-scale multi-national projects like the forthcoming analysis of the LHC particle collision data at CERN relies to a great extent on the ability to efficiently utilize computing a management software (Datagrid, Globus, etc.), while the effective integration of computing nodes has been largely neglected up to now. This is the focus of our work. We present a framework for a high-performance cluster that can be used as a reliable computing node in the Grid. We outline the cluster architecture, the management of distributed data and the seamless intergration of the cluster into the Grid environment.

Description: Der Aufsatz ist die ausgearbeitete Fassung eines Vortrages, gehalten am 05.04.2001 auf dem 91. Deutschen Bibliothekartag in Bielefeld. Der Kooperative Bibliotheksverbund Berlin-Brandenburg (KOBV) ist im Rahmen eines wissenschaftlichen Projektes in den Jahren 1997 bis 2000 am Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB) aufgebaut worden. Nachdem das Projekt erfolgreich abgeschlossen ist, wird der KOBV 2001 institutionalisiert. In dem Vortrag hat die Verfasserin einen Überblick über das bisher Erreichte, den derzeitigen Stand und die Perspektiven des neuen Verbundes gegeben. Der KOBV stellt eine neue Art von Bibliotheksverbund dar. Sein technisches Konzept und sein organisatorischer Aufbau basieren auf der {\sl Internetphilosophie}. Den informationstechnischen Kern bildet eine Suchmaschine, die die heterogenen lokalen Bibliothekssysteme miteinander verbindet. Die KOBV-Organisation ist dezentral. Sie wird getragen von der Kooperation der Bibliotheken in Berlin und Brandenburg. Eine kleine Verbundzentrale koordiniert dieses Geflecht vernetzter lokaler Einheiten, vertritt den KOBV nach außen und arbeitet - in Form von Projekten - an seiner Weiterentwicklung. Der Entwicklungsaspekt und die Nutzerorientierung sind zwei wesentliche Komponenten in der Verbundarbeit. Berlin und Brandenburg haben auf engem Raum zahlreiche Bibliotheken mit großen, reichhaltigen Medienbeständen. Mittel- bis langfristig sollen Bibliotheken aller Sparten und Größen in den KOBV integriert werden, seien es wissenschaftliche Universalbibliotheken, universitäre Bibliothekssysteme, Spezialbibliotheken, Behörden- und Parlamentsbibliotheken oder öffentliche Bibliotheken. Auch regionale Bibliotheksverbünde können als Subverbünde am KOBV teilnehmen. Mit der KOBV-Suchmaschine ist eine offene Plattform geschaffen worden, auf der weitere Entwicklungen aufsetzen können. Der Aufbau einer virtuellen Regionalbibliothek mit Bestell- und Lieferkomponenten ist eines der Ziele. Darüber hinaus ist es die Vision, in der Region ein virtuelles {\sl Wissensportal} aufzubauen, das dem Nutzer unter einer Adresse den umfassenden Zugang und die umfassende Bereitstellung von Informationen aller Art bietet.

Description: A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem.

Description: Das \emph{Committee on Electronic Information and Communication} (CEIC) der \emph{International Mathematical Union} (IMU) hat die Aufgabe, sich über die langfristige Informationsversorgung in der Mathematik Gedanken zu machen und Lösungsvorschläge hierfür zu erarbeiten. Das Kernthema ist natürlich "`Elektronisches Publizieren"'. Dazu gehören auch Copyright-Regelungen. % Sie sind -- % neben einer Andeutung der weiteren CEIC-Pläne -- der Fokus dieses % kurzen Artikels. Er schließt mit einem von der IMU verabschiedeten % Aufruf zu vernünftigem Verhalten bei Copyright-Vereinbarungen. Eine % nachhaltige Befolgung dieses Aufrufs -- verbunden mit weiteren % Aktivitäten -- könnte die (derzeit kaum noch bezahlbare und % dadurch gefährdete) Literaturversorgung nachhaltig zum Positiven % verändern. Mit diesem Artikel beginnt eine kleine Serie von Aufsätzen, in denen ich (in meiner Funktion als eines von elf CEIC-Mitgliedern) die Empfehlungen des CEIC erläutern werde. % Das heutige Thema sind die % CEIC-Vorschläge zum Copyright

Description: By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method.

Description: Optimization is the task of finding an optimum solution to a given problem. When the decision variables are discrete we speak of a combinatorial optimization problem. Such a problem is online when decisions have to be made before all data of the problem are known. And we speak of a real-time online problem when online decisions have to be computed within very tight time bounds. This paper surveys the are of combinatorial online and real-time optimization, it discusses, in particular, the concepts with which online and real-time algorithms can be analyzed.

Description: This paper describes a new simulation tool for the prediction of aerosol formation and behavior in gas--liquid contact devices such as absorbers, scrubbers, quench coolers, and condensers as well as multistage gas cleaning processes, respectively. Aerosol formation can impact severely the separation efficiency of gas cleaning processes. Aerosol or fog formation can arise by spontaneous condensation or desublimation in supersaturated gas phases. The rigorous description of the mass and energy transfer between the gas phase, the liquid phase, and the growing aerosol droplets leads to a system of partial differential and algebraic equations. For the solution of these systems we have developed the plant simulation tool AerCoDe. This program bases upon the linearly--implicit Euler discretisation, which in combination with extrapolation permits an adaptive step size and order control. Typical simulation results of a multistage industrial flue gas scrubbing process are presented. It is shown, that experimental data can be confirmed if the number concentration of condensation nuclei as an input parameter is roughly known.

Description: This paper discusses online optimization of real-world transportation systems. We concentrate on transportation problems arising in production and manufacturing processes, in particular in company internal logistics. We describe basic techniques to design online optimization algorithms for such systems, but our main focus is decision support for the planner: which online algorithm is the most appropriate one in a particular setting? We show by means of several examples that traditional methods for the evaluation of online algorithms often do not suffice to judge the strengths and weaknesses of online algorithms. We present modifications of well-known evaluation techniques and some new methods, and we argue that the selection of an online algorithm to be employed in practice should be based on a sound combination of several theoretical and practical evaluation criteria, including simulation.

Description: Wireless communication networks employ radio frequencies to establish communication links. The available radio spectrum is very limited. To meet today's radio communication demand, this resource has to be administered and reused carefully in order to control mutual interference. The reuse can be organized via separation in space, time, or frequency, for example. The problem, therefore, arises to distribute frequencies to links in a ``reasonable manner''. This is the basic form of the frequency assignment problem. What ``reasonable'' means, how to quantify this measure of quality, which technical side constraints to consider cannot be answered in general. The exact specification of this task and its mathematical model depend heavily on the particular application considered. In this paper we discuss this issue with respect to the GSM standard for mobile communication.

Description: This paper is a summary of the Round Table: ``The Impact of Mathematical Research on Industry and Vice Versa'' held at 3ecm in Barcelona on July 11, 2000. The round table started with contributions of the three panelists. Irene Fonseca, the panel chair, opened the discussion by stating six questions addressing the main issues of the round table topic. She presented the panel's answers to these questions, drawing on many examples from her own academic experience. In the following additional presentations, the other two panel members added further points of view based on their personal involvement with industry. The round table ended with a lively discussion with members from the audience. This written summary of the oral presentations follows the structure of the round table indicated above.

Description: This article is about \emph{adaptive column generation techniques} for the solution of duty scheduling problems in public transit. The current optimization status is exploited in an adaptive approach to guide the subroutines for duty generation, LP resolution, and schedule construction toward relevant parts of a large problem. Computational results for three European scenarios are reported.

Description: The recent spectral bundle method allows to compute, within reasonable time, approximate dual solutions of large scale semidefinite quadratic 0-1 programming relaxations. We show that it also generates a sequence of primal approximations that converge to a primal optimal solution. Separating with respect to these approximations gives rise to a cutting plane algorithm that converges to the optimal solution under reasonable assumptions on the separation oracle and the feasible set. We have implemented a practical variant of the cutting plane algorithm for improving semidefinite relaxations of constrained quadratic 0-1 programming problems by odd-cycle inequalities. We also consider separating odd-cycle inequalities with respect to a larger support than given by the cost matrix and present a heuristic for selecting this support. Our preliminary computational results for max-cut instances on toroidal grid graphs and balanced bisection instances indicate that warm start is highly efficient and that enlarging the support may sometimes improve the quality of relaxations considerably.

Description: Der Wissenschaftsrat hat in seiner Juli-Sitzung 2001 \glqq Empfehlungen zur digitalen Informationsversorgung durch Hochschulbibliotheken \grqq verabschiedet. Einige der Vorschläge des Wissenschaftsrates können, falls sie von den angesprochenen Institutionen aufgenommen werden, zu einer nachhaltigen Veränderung der wissenschaftlichen Informationslandschaft führen. In meinem kurzen Kommentar zu diesem Papier möchte ich auf einige dieser Anregungen hinweisen.

Description: Von welcher "Informationsumwelt" träumt jemand, der für seine wissenschaftliche (und sonstige) Arbeit digitale Informationstechnologie intensiv einsetzt? In diesem Artikel beschreibe ich meinen "digitalen Traum". Er ist ganz einfach zu formulieren:"Ich will alles und zwar sofort, jederzeit, "überall" und kostenlos zur Verfügung haben." Ich schildere, was davon heute schon (fast) realisiert ist und was noch fehlt. Ich skizziere einige zentrale Schwierigkeiten der vollständigen Realisierung und skizziere mögliche Lösungen.

Description: Im Rahmen der biomechanischen Simulation knöcherner Organe ist die Frage nach einer befriedigenden Materialbeschreibung nach wie vor ungelöst. Computertomographische Datensätze liefern eine räumliche Verteilung der (Röntgen-)Dichte und ermöglichen damit eine gute Darstellung der individuellen Geometrie. Weiter können die verschiedenen Materialbestandteile des Knochens, Spongiosa und Kortikalis, voneinander getrennt werden. Aber die richtungsabängige Information der Materialanisotropie ist verloren. In dieser Arbeit wird ein Ansatz für eine anisotrope Materialbeschreibung vorgestellt, die es ermöglicht, den Einfluss der individuellen knöchernen Struktur auf das makroskopische Materialverhalten abzuschätzen.