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- Christian Liebchen, Marco E. Lübbecke, Rolf H. Möhring, Sebastian Stiller
- Robust and Online Large-Scale Optimization
- 2009

We present a new concept for optimization under uncertainty: recoverable robustness. A solution is recovery robust if it can be recovered by limited means in all likely scenarios. Specializing the general concept to linear programming we can show that recoverable robustness combines the flexibility of stochastic programming with the tractability and… (More)

- Christian Liebchen, Romeo Rizzi
- Inf. Process. Lett.
- 2005

We consider the problem of computing a minimum cycle basis of a directed graph with m arcs and n nodes. We adapt the greedy approach proposed by Horton [A polynomial-time algorithm to find the shortest cycle basis of a graph, SIAM J. Comput. 16 (1987) 358] and hereby obtain a very simple exact algorithm of complexity Õ(m4n), being as fast as the first… (More)

- Telikepalli Kavitha, Christian Liebchen, +4 authors Katharina Anna Zweig
- Computer Science Review
- 2009

Cycles in graphs play an important role in many applications, e.g., analysis of electrical networks, analysis of chemical and biological pathways, periodic scheduling, and graph drawing. From a mathematical point of view, cycles in graphs have a rich structure. Cycle bases are a compact description of the set of all cycles of a graph. In this paper, we… (More)

- Christian Liebchen
- OR
- 2006

To my family—in particular to Annika and to our three children. .. Preface Well, " is this really a math book " ? This is the question the reader might have in mind until Proposition 4.2 on Page 31. Indeed, the first chapters—as well as the very last one—address a very general readership, including scientists and practitioners in traffic engineering and… (More)

- Christian Liebchen, Rolf H. Möhring
- ATMOS
- 2004

In the planning process of railway companies, we propose to integrate important decisions of network planning, line planning, and vehicle scheduling into the task of periodic timetabling. From such an integration, we expect to achieve an additional potential for optimization. Models for periodic timetabling are commonly based on the Periodic Event… (More)

- Christian Liebchen, Romeo Rizzi
- Discrete Applied Mathematics
- 2007

In the last years, new variants of the minimum cycle basis (MCB) problem and new classes of cycle bases have been introduced, as motivated by several applications from disparate areas of scientific and technological inquiries. At present, the complexity status of the MCB problem has been settled only for undirected, directed, and strictly fundamental cycle… (More)

- Christian Liebchen
- Transportation Science
- 2008

Station period time Trips covering the time slice Osloer Straße Departure xxx1 2031 2041 · · · 2341 2351 Zoologischer Garten Arrival xxx2 2042 2052 · · · 2352 0002 Departure xxx2 2042 2052 · · · 2352 0002 Kurfürstendamm Arrival xxx4 2044 2054 · · · 2354 0004 Departure xxx4 2044 2054 · · · 2354 0004 Rathaus Steglitz Arrival xxx4 2054 2104 · · · 0004 0014 The… (More)

- Christian Liebchen
- ESA
- 2003

Cyclic timetabling for public transportation companies is usually modeled by the periodic event scheduling problem. To deduce a mixed-integer programming formulation, artificial integer variables have to be introduced. There are many ways to define these integer variables. We show that the minimal number of integer variables required to encode an instance… (More)

- Christian Liebchen, Michael Schachtebeck, Anita Schöbel, Sebastian Stiller, André Prigge
- Computers & OR
- 2010

In the past, much research has been dedicated to compute optimum railway timetables. A typical objective was the minimization of passenger waiting times. But only the planned nominal waiting times were addressed, whereas delays, as they occur in daily operations, were neglected. Delays were rather treated mainly in an online-context, and solved as a… (More)

- Christian Liebchen, Sebastian Stiller
- Public Transport
- 2009