@misc{BorndoerferKarbstein, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {A Note on Menger's Theorem for Hypergraphs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14471}, number = {12-03}, abstract = {We prove the companion Theorem to Menger's Theorem for hypergraphs. This result gives rise to a new class of blocking pairs of ideal matrices, that generalize the incidence matrices of cuts and paths.}, language = {en} } @misc{BorndoerferFriedowKarbstein, author = {Bornd{\"o}rfer, Ralf and Friedow, Isabel and Karbstein, Marika}, title = {Optimierung des Linienplans 2010 in Potsdam}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14486}, number = {12-04}, abstract = {Im Zuge der {\"U}bernahme von 6 Linien der Havelbus Verkehrsgesellschaft mbH durch die ViP Verkehr in Potsdam GmbH ergab sich 2009 die Notwendigkeit der Entwicklung eines neuen Linien- und Taktplans f{\"u}r das Jahr 2010. Das Konrad-Zuse-Zentrum f{\"u}r Informationstechnik Berlin (ZIB) entwickelt in einem Projekt des DFG-Forschungszentrums Matheon ein Verfahren zur mathematischen Linienoptimierung. Dieses Tool wurde bei der Optimierung des ViP Linienplans 2010 in einer projektbegleitenden Studie eingesetzt, um Alternativen bei verschiedenen Planungs- und Zielvorgaben auszuloten. In dem Artikel wird eine Auswertung der Ergebnisse mit dem Verkehrsanalysesystem Visum der PTV AG beschrieben. Die Auswertungen best{\"a}tigen, dass mit Hilfe von mathematischer Optimierung eine weitere Verk{\"u}rzung der Reisezeit um 1\%, eine als um 6\% verk{\"u}rzt empfundene Reisezeit, 10\% weniger Fahrzeit im Fahrzeug und eine gleichzeitige Kostenreduktion um 5\% m{\"o}glich sind.}, language = {de} } @inproceedings{BorndoerferKarbstein, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {A Direct Connection Approach to Integrated Line Planning and Passenger Routing}, series = {ATMOS 2012 - 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, volume = {25}, booktitle = {ATMOS 2012 - 12th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, editor = {Delling, Daniel and Liberti, Leo}, doi = {http://dx.doi.org/10.4230/OASIcs.ATMOS.2012.47}, pages = {47 -- 57}, language = {en} } @article{BorndoerferFriedowKarbstein, author = {Bornd{\"o}rfer, Ralf and Friedow, Isabel and Karbstein, Marika}, title = {Optimierung des Linienplans 2010 in Potsdam}, series = {Der Nahverkehr}, volume = {30}, journal = {Der Nahverkehr}, number = {4}, pages = {34 -- 39}, language = {de} } @article{BorndoerferKarbsteinPfetsch, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Pfetsch, Marc}, title = {Models for Fare Planning in Public Transport}, series = {Discrete Applied Mathematics}, volume = {160}, journal = {Discrete Applied Mathematics}, number = {18}, doi = {10.1016/j.dam.2012.02.027}, pages = {2591 -- 2605}, language = {en} } @misc{BorndoerferKarbstein, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika}, title = {A Direct Connection Approach to Integrated Line Planning and Passenger Routing}, series = {ATMOS 2012 - 12th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, volume = {25}, journal = {ATMOS 2012 - 12th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, editor = {Delling, Daniel and Liberti, Leo}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"u}r Informatik}, issn = {1438-0064}, doi = {http://dx.doi.org/10.4230/OASIcs.ATMOS.2012.47}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-15812}, pages = {47 -- 57}, abstract = {The treatment of transfers is a major challenge in line planning. Existing models either route passengers and lines sequentially, and hence disregard essential degrees of freedom, or they are of extremely large scale, and seem to be computationally intractable. We propose a novel direct connection approach that allows an integrated optimization of line and passenger routing, including accurate estimates of the number of direct travelers, for large-scale real-world instances.}, language = {en} } @inproceedings{BorndoerferHoppmannKarbstein, author = {Bornd{\"o}rfer, Ralf and Hoppmann, Heide and Karbstein, Marika}, title = {A Configuration Model for the Line Planning Problem}, series = {ATMOS 2013 - 13th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, volume = {33}, booktitle = {ATMOS 2013 - 13th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems}, editor = {Frigioni, Daniele and Stiller, Sebastian}, publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik}, doi = {10.4230/OASIcs.ATMOS.2013.68}, pages = {68 -- 79}, language = {en} } @incollection{BorndoerferHoangKarbsteinetal., author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Karbstein, Marika and Koch, Thorsten and Martin, Alexander}, title = {How many Steiner terminals can you connect in 20 years?}, series = {Facets of Combinatorial Optimization; Festschrift for Martin Gr{\"o}tschel}, booktitle = {Facets of Combinatorial Optimization; Festschrift for Martin Gr{\"o}tschel}, editor = {J{\"u}nger, Michael and Reinelt, Gerhard}, publisher = {Springer}, doi = {10.1007/978-3-642-38189-8_10}, pages = {215 -- 244}, language = {en} } @misc{BorndoerferHoangKarbsteinetal., author = {Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Karbstein, Marika and Koch, Thorsten and Martin, Alexander}, title = {How Many Steiner Terminals Can You Connect in 20 Years?}, issn = {1438-0064}, doi = {10.1007/978-3-642-38189-8_10}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42524}, abstract = {Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful approaches to many relevant variants, from both a theoretical and a computational point of view. This article illustrates the theoretical and algorithmic progress on Steiner tree type problems on two examples, the Steiner connectivity and the Steiner tree packing problem.}, language = {en} } @article{BorndoerferKarbsteinPfetsch, author = {Bornd{\"o}rfer, Ralf and Karbstein, Marika and Pfetsch, Marc}, title = {The Steiner connectivity problem}, series = {Mathematical Programming A}, volume = {142}, journal = {Mathematical Programming A}, number = {1}, doi = {10.1007/s10107-012-0564-5}, pages = {133 -- 167}, language = {en} }