TY - GEN A1 - Rambau, Jörg T1 - Circuit Admissible Triangulations of Oriented Matroids N2 - All triangulations of euclidean oriented matroids are of the same PL-homeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PL-spheres. For non-euclidean oriented matroids this question is wide open. One key point in the proof of Anderson is the following fact: for every triangulation of a euclidean oriented matroid the adjacency graph of the set of all simplices ``intersecting'' a segment $[p_-p_+]$ is a path. We call this graph the $[p_-p_+]$-adjacency graph of the triangulation. While we cannot solve the problem of the topological type of triangulations of general oriented matroids we show in this note that for every circuit admissible triangulation of an arbitrary oriented matroid the $[p_-p_+]$-adjacency graph is a path. T3 - ZIB-Report - 00-45 KW - triangulations of oriented matroids KW - topological type KW - segment adjacency graph Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6139 ER - TY - GEN A1 - Rambau, Jörg T1 - Triangulierungen von Punktmengen und Polyedern N2 - Dieser Report wurde im Sommersemester 2000 an der TU Berlin in einer Spezialvorlesung über Triangulierungen von Punktmengen und Polyedern als Skriptum verwendet. Nach einem motivierenden Kapitel werden grundlegende Begriffe und Konstruktionen in der Theorie der Triangulierungen von Punktmengen und Polyedern vorgestellt. Danach werden als weiterführende Themen reguläre Triangulierungen, Sekundärpolytope, bistellare Operationen, höhere Stasheff-Tamari-Halbordnungen und Triangulierungen mit wenigen bzw. gar keinen Flips behandelt. Ein Kapitel über Enumeration und Optimierung beschließt die Zusammenstellung. T3 - ZIB-Report - 00-46 KW - point configuration KW - triangulation KW - polytope KW - polyhedron KW - Gale diagram KW - secondary polytope KW - cyclic polytope KW - graph of all triangulations KW - conn Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6145 ER - TY - GEN A1 - Hülsermann, Ralf A1 - Jäger, Monika A1 - Krumke, Sven A1 - Poensgen, Diana A1 - Rambau, Jörg A1 - Tuchscherer, Andreas T1 - Dynamic Routing Algorithms in Transparent Optical Networks An Experimental Study Based on Real Data N2 - 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. T3 - ZIB-Report - 02-35 KW - Dynamic Network Configuration KW - Routing and Wavelength Allocation KW - Transparent Optical Networks KW - Blocking Probability KW - Simulation Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7025 ER - TY - GEN A1 - Rambau, Jörg T1 - TOPCOM: Triangulations of Point Configurations and Oriented Matroids N2 - 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. T3 - ZIB-Report - 02-17 KW - triangulation KW - point configuration KW - oriented matroid KW - software KW - chirotope KW - circuit KW - cocircuit KW - symmetry KW - TOPCOM Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6849 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Torres, Luis Miguel T1 - Making the Yellow Angels Fly: Online Dispatching Of Service Vehicles in Real Time N2 - 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. T3 - ZIB-Report - 02-18 KW - vehicle dispatching KW - soft time windows KW - real-time KW - column generation KW - pricing KW - branch and bound KW - real world data KW - ADAC Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6858 ER - TY - GEN A1 - Krumke, Sven A1 - Lipmann, Maarten A1 - Paepe, Willem de A1 - Poensgen, Diana A1 - Rambau, Jörg A1 - Stougie, Leen A1 - Woeginger, Gerhard T1 - How to Cut a Cake Almost Fairly N2 - 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. T3 - ZIB-Report - 02-23 KW - Fair division KW - cake cutting Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6905 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Winter, Thomas A1 - Zimmermann, Uwe T1 - Combinatorial Online Optimization in Real Time N2 - 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. T3 - ZIB-Report - 01-16 KW - Online Optimization KW - Realtime Optimization KW - Competitive Analysis KW - Heuristics KW - Survey Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6424 ER - TY - GEN A1 - Grötschel, Martin A1 - Krumke, Sven A1 - Rambau, Jörg T1 - Online Optimization of Complex Transportation Systems N2 - 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. T3 - ZIB-Report - 01-17 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6438 ER - TY - GEN A1 - Krumke, Sven A1 - Rambau, Jörg A1 - Torres, Luis Miguel T1 - Real-Time Dispatching of Guided and Unguided Automobile Service Units with Soft Time Windows N2 - 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. T3 - ZIB-Report - 01-22 KW - vehicle dispatching KW - soft time windows KW - real-time KW - column generation KW - pricing KW - branch and bound KW - real world data KW - ADAC Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6484 ER - TY - GEN A1 - Krumke, Sven A1 - Paepe, Willem de A1 - Rambau, Jörg A1 - Stougie, Leen T1 - Online Bin-Coloring N2 - 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. T3 - ZIB-Report - 01-07 KW - Online Optimization KW - randomized algorithms KW - lower bounds KW - competitive analysis Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6338 ER -