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The Cycle Embedding Problem

In: Operations Research Proceedings 2014

Author

Listed:
  • Ralf Borndörfer

    (Zuse Institute Berlin)

  • Marika Karbstein

    (Zuse Institute Berlin)

  • Julika Mehrgardt

    (Zuse Institute Berlin)

  • Markus Reuther

    (Zuse Institute Berlin)

  • Thomas Schlechte

    (Zuse Institute Berlin)

Abstract

Given two hypergraphs, representingBorndörfer, Ralf a fineKarbstein, Marika and a coarseMehrgardt, Julika “layer”, and a cycleReuther, Markus coverSchlechte, Thomas 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.

Suggested Citation

  • Ralf Borndörfer & Marika Karbstein & Julika Mehrgardt & Markus Reuther & Thomas Schlechte, 2016. "The Cycle Embedding Problem," Operations Research Proceedings, in: Marco Lübbecke & Arie Koster & Peter Letmathe & Reinhard Madlener & Britta Peis & Grit Walther (ed.), Operations Research Proceedings 2014, edition 1, pages 465-471, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-28697-6_65
    DOI: 10.1007/978-3-319-28697-6_65
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