The Cycle Embedding Problem

  • Ralf Borndörfer
  • Marika Karbstein
  • Julika Mehrgardt
  • Markus Reuther
  • Thomas Schlechte
Conference paper
Part of the Operations Research Proceedings book series (ORP)


Given two hypergraphs, representing a fine and a coarse “layer”, and a cycle cover of the nodes of the coarse layer, the cycle embedding problem (CEP) asks for an embedding of the coarse cycles into the fine layer. The CEP is NP-hard for general hypergraphs, but it can be solved in polynomial time for graphs. We propose an integer programming formulation for the CEP that provides a complete description of the CEP polytope for the graphical case. The CEP comes up in railway vehicle rotation scheduling. We present computational results for problem instances of DB Fernverkehr AG that justify a sequential coarse-first-fine-second planning approach.


  1. 1.
    Mehrgardt, J.: Kreiseinbettungen in Hypergraphen. Master’s thesis, TU Berlin, Feb 2013Google Scholar
  2. 2.
    Markus Reuther, Ralf Borndörfer, and Thomas Schlechte.: A coarse-to-fine approach to the railway rolling stock rotation problem. In 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2014, September 11, 2014, Wroclaw, Poland, pages 79–91, 2014Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Zuse Institute BerlinBerlinGermany

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