Christian Liebchen

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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)
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)
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)
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)
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)
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)
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)
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)