@misc{KrumkeRambauWeider, author = {Krumke, Sven and Rambau, J{\"o}rg and Weider, Steffen}, title = {An Approximation Algorithm for the Non-Preemptive Capacitated Dial-a-Ride Problem}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6217}, number = {00-53}, abstract = {In the Capacitated Dial-a-Ride Problem (CDARP) we are given a transportation network and a finite set of transportation jobs. Each job specifies the source and target location which are both part of the network. A server which can carry at most \$C\$~objects at a time can move on the transportation network in order to process the transportation requests. The problem CDARP consists of finding a shortest transportation for the jobs starting and ending at a designated start location. In this paper we are concerned with the restriction of CDARP to graphs which are simple paths. This setting arises for instance when modelling applications in elevator transportation systems. It is known that even for this restricted class of graphs CDARP is NP-hard to solve. We provide a polynomial time approximation algorithm that finds a transportion of length at most thrice the length of the optimal transportation.}, language = {en} } @misc{Rambau, author = {Rambau, J{\"o}rg}, title = {Circuit Admissible Triangulations of Oriented Matroids}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6139}, number = {00-45}, abstract = {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.}, language = {en} } @misc{AscheuerGroetschelKrumkeetal., author = {Ascheuer, Norbert and Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Combinatorial Online Optimization}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3674}, number = {SC-98-24}, abstract = {In ``classical'' optimization, all data of a problem instance are considered given. The standard theory and the usual algorithmic techniques apply to such cases only. Online optimization is different. Many decisions have to be made before all data are available. In addition, decisions once made cannot be changed. How should one act ``best'' in such an environment? In this paper we survey online problems coming up in combinatorial optimization. We first outline theoretical concepts, such as competitiveness against various adversaries, to analyze online problems and algorithms. The focus, however, lies on real-world applications. We report, in particular, on theoretical investigations and our practical experience with problems arising in transportation and the automatic handling of material.}, language = {en} } @inproceedings{AscheuerGroetschelKrumkeetal.1999, author = {Ascheuer, Norbert and Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg}, title = {Combinatorial Online Optimization}, series = {Operations Research Proceedings 1998. Selected Papers of the International Conference on Operations Research Zurich, August 31 - September 3, 1998}, booktitle = {Operations Research Proceedings 1998. Selected Papers of the International Conference on Operations Research Zurich, August 31 - September 3, 1998}, editor = {Kall, Peter and L{\"u}thi, Hans-Jakob}, publisher = {Springer}, pages = {21 -- 37}, year = {1999}, language = {en} } @misc{AscheuerGroetschelKaminetal., author = {Ascheuer, Norbert and Gr{\"o}tschel, Martin and Kamin, Nicola and Rambau, J{\"o}rg}, title = {Combinatorial Online Optimization in Practice}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3508}, number = {SC-98-07}, abstract = {This paper gives a short introduction into combinatorial online optimization. It explains a few evaluation concepts of online algorithms, such as competitiveness, and discusses limitations in their application to real--world problems. The main focus, however, is a survey of combinatorial online problems coming up in practice, in particular, in large scale material flow and flexible manufacturing systems.}, language = {en} } @article{AscheuerGroetschelKaminetal.1998, author = {Ascheuer, Norbert and Gr{\"o}tschel, Martin and Kamin, Nicola and Rambau, J{\"o}rg}, title = {Combinatorial online optimization in practice}, series = {OPTIMA}, volume = {57}, journal = {OPTIMA}, pages = {1 -- 6}, year = {1998}, language = {en} } @misc{GroetschelKrumkeRambauetal., author = {Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg and Winter, Thomas and Zimmermann, Uwe}, title = {Combinatorial Online Optimization in Real Time}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6424}, number = {01-16}, abstract = {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.}, language = {en} } @incollection{GroetschelKrumkeRambauetal.2001, author = {Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg and Winter, Thomas and Zimmermann, Uwe}, title = {Combinatorial Online Optimization in Real Time}, series = {Online Optimization of Large Scale Systems}, booktitle = {Online Optimization of Large Scale Systems}, editor = {Gr{\"o}tschel, Martin and Krumke, Sven and Rambau, J{\"o}rg}, publisher = {Springer}, pages = {679 -- 704}, year = {2001}, language = {en} } @misc{PfeifleRambau, author = {Pfeifle, Julian and Rambau, J{\"o}rg}, title = {Computing Triangulations Using Oriented Matroids}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6692}, number = {02-02}, abstract = {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.}, language = {en} } @inproceedings{HuelsermannJaegerPoensgenetal.2003, author = {H{\"u}lsermann, Ralf and J{\"a}ger, Monika and Poensgen, Diana and Krumke, Sven and Rambau, J{\"o}rg and Tuchscherer, Andreas}, title = {Dynamic routing algorithms in transparent optical networks}, series = {Proceedings of the 7th IFIP Working Conference on Optical Network Design \& Modelling (ONDM 2003)}, booktitle = {Proceedings of the 7th IFIP Working Conference on Optical Network Design \& Modelling (ONDM 2003)}, editor = {Cinkler, Tibor and Jakab, Tivadar and Tapolcai, J{\`a}nos and G{\`a}sp{\`a}r, Csaba}, publisher = {Kluwer Academic Press}, pages = {293 -- 312}, year = {2003}, language = {en} }