The Transitive Minimum Manhattan Subnetwork Problem in 3 Dimensions

We consider the Minimum Manhattan Subnetwork (MMSN) Problem which generalizes the already known Minimum Manhattan Network (MMN) Problem: Given a set P of n points in the plane, find shortest rectilinear paths between all pairs of points. These paths form a network, the total length of which has to be minimized. From a graph theoretical point of view, a MMN is a 1-spanner with respect to the L_1 metric. In contrast to the MMN problem, a solution to the MMSN problem does not demand L_1 -shortest paths for all point pairs, but only for a given set R subseteq P imes P of pairs. The complexity status of the MMN problem is still unsolved in geq 2 dimensions, whereas the MMSN was shown to be NP -complete considering general relations R in the plane. We restrict the MMSN problem to transitive relations R_T ({em Transitive} Minimum Manhattan Subnetwork (TMMSN) Problem) and show that the TMMSN problem is Max-SNP -complete with epsilon<frac{1}{8} in 3 dimensions

The Transitive Minimum Manhattan Subnetwork Problem in 3 Dimensions

We consider the Minimum Manhattan Subnetwork (MMSN) Problem which generalizes the already known Minimum Manhattan Network (MMN) Problem: Given a set P of n points in the plane, find shortest rectilinear paths between all pairs of points. These paths form a network, the total length of which has to be minimized. From a graph theoretical point of view, a MMN is a 1-spanner with respect to the L_1 metric. In contrast to the MMN problem, a solution to the MMSN problem does not demand L_1 -shortest paths for all point pairs, but only for a given set R subseteq P imes P of pairs. The complexity status of the MMN problem is still unsolved in geq 2 dimensions, whereas the MMSN was shown to be NP -complete considering general relations R in the plane. We restrict the MMSN problem to transitive relations R_T ({em Transitive} Minimum Manhattan Subnetwork (TMMSN) Problem) and show that the TMMSN problem is Max-SNP -complete with epsilon<frac{1}{8} in 3 dimensions

A Generalized Flow Network for Freight Car Dispatching

In the freight car dispatching problem empty freight cars have to be assigned to known demands respecting a given time horizon and certain constraints. The goal is to minimize the resulting transportation costs. One of the constraints is that customers can specify the type of cars they want. It is possible, however, that cars of certain types can be substituted by other cars either in a 1-to-1 fashion or at different exchange rates. We show that these substitutions make the dispatching problem NP-complete. We model the dispatching problem as a generalized integral minimum cost flow problem on a specific directed graph. We show that in our setting its linear relaxation is half-integral. Using rounding techniques, the LP-relaxation can be transformed to a dispatching with small constraint violation at the same cost, or, under additional assumptions, to a 4 -approximation. In practice, both ideas are combined to a heuristic approach without further assumptions. We conclude with computational results for this heuristic on application data provided by DB Schenker Rail Deutschland AG in context of a joint R-and-D project together with the Technical University of Kaiserslautern

A Note on the Complexity of Sliding Shortest Paths

We address a shortest path problem in a given uncapacited and undirected network N=(V,E) with positive edge costs. In addition we are given a single source-destination pair (s,t), a shortest path p{st} connecting s and t and a new edge e =(p,q). The task is to find a minimum number of edges Ec and the minimum weight increase for each edge e in Ec such that the shortest path p{st} between s and t traverses edge e. We show that the problem is NP-hard and give a heuristic scheme for the problem

A Note on the Complexity of Sliding Shortest Paths

We address a shortest path problem in a given uncapacited and undirected network N=(V,E) with positive edge costs. In addition we are given a single source-destination pair (s,t), a shortest path p{st} connecting s and t and a new edge e =(p,q). The task is to find a minimum number of edges Ec and the minimum weight increase for each edge e in Ec such that the shortest path p{st} between s and t traverses edge e. We show that the problem is NP-hard and give a heuristic scheme for the problem

A Generalized Network Model for Freight Car Distribution

We consider the empty freight car distribution problem (DP) at DB Schenker Rail Deutschland AG under a wide range of application relevant constraints and real data sets. The (DP) is an online assignment problem between geographically distributed empty freight car supplies and customer demands for such cars in preparation of good transport. The objective is to minimize transport costs for empty cars while distributing them effectively with respect to the constraints. In our case, one major constraint is given by prescheduled freight trains: obviously a supply can only be assigned to a demand if it reaches the latter in time. Further, the variety of goods (bulk cargo, steel coils, etc.) to be transported requires distinct types of freight cars. Freight cars of a certain type can be exchanged by cars of other types with respect to a given substitution scheme and different 'exchange rates'. Allowed substitutions are therefore another major constraint of the (DP). We describe further `hard' and `soft' constraints and sketch the current work flow at DB Schenker Rail Deutschland AG to find an adequate solution for the (DP) on a daily base in practice. The (DP) is currently solved separately for groups of car types and in several steps. Moreover, some steps contain manual pre- and post-processing to ensure certain constraints. Hence global sub-optimal distributions can occur. We therefore integrate all constraints into a generalized network flow model for the (DP). A global optimal distribution is then provided by an integral minimum cost flow in the network. To find such a flow is NP-hard in general. We show that a general substitution scheme makes our notion of the (DP) also NP-hard. Hence independent of the applied model and with respect to practical runtime requirements, we have to find a compromise between solution time and quality. We do so in two ways. Instances of the (DP) which correspond to classical flow networks are solved by an integral minimum cost flow, which can be obtained in polynomial time. We use such instances to polynomially obtain minimum cost flows of fixed bounded fractionality for certain general instances. For those instances occurring in the application we obtain half-integral flows, which can be rounded to approximate or heuristic distributions in linear time. Moreover, we develop a network-based reoptimization approach, which yields optimal solutions for subsequent instances with few changes very fast. This thesis was inspired and funded by a 2-year research and development project of DB Schenker Rail Deutschland AG in cooperation with the work group Faigle/Schrader of the University of Cologne and the work group of Prof. Dr. Sven O. Krumke at the Technical University of Kaiserslautern. The project included the implementation of the generalized network model and the reoptimization, approximation and heuristic methods. The software is designed as a future optimization kernel for the (DP) at DB Schenker Rail Deutschland AG

Integer Flows with Multipliers 1 and 2

The problem to find a valid Integer generalized flow is long known to be NP-complete (S. Sahni, 1974). We show that the problem is still hard restricted to multipliers 1 and 2 and that optimal solutions with (almost) arbitrary fractions can occur. In some (still NP-hard) application motivated network instances optimal solutions are halfintegral. To solve the latter (optimally) we modify the Successive Shortest Path Algorithm and try to (heuristically) find acceptable integral solutions

Einführung des cloudbasierten Bibliothekssystems Alma in Berlin – ein Erfahrungsbericht

Die enge Zusammenarbeit der vier Berliner Universitätsbibliotheken [Freie Universität Berlin (FU), Humboldt-Universität zu Berlin (HU), Technische Universität Berlin (TU), Universität der Künste Berlin (UdK)] reicht weit zurück. Bereits vor der Jahrtausendwende haben die Berliner Universitätsbibliotheken (UBs) gemeinsam das Bibliothekssystem Aleph 500 ausgewählt und implementiert, danach folgten weitere Systeme – das Linking System SFX, die Digitale Bibliothek MetaLib und das Bibliotheksportal Primo. Es war daher folgerichtig und selbstverständlich, dass auch die Auswahl und Implementierung eines neuen Bibliothekssystems in enger Abstimmung und Zusammenarbeit erfolgte. Die Erfahrungen bei Vertragsverhandlungen und Implementierung von Alma sind Gegenstand des folgenden Berichtes.As regards implementing new library technology, the Berlin University libraries have been working closely together for more than 20 years. It was the case for the implementation of the legacy system Aleph 500, the linking system SFX, the digital library MetaLib and the library portal Primo, and therefore it was a matter of course to continue the close cooperation during the implementation of the new cloud-based library system, too. The experience gained during the contract negotiations and the implementation project, and lessons learned are the focus of this report.Peer Reviewe