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A Hypergraph Network Simplex Algorithm

In: Operations Research Proceedings 2017

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  • Isabel Beckenbach

    (Zuse Institute Berlin)

Abstract

We describe a network simplex algorithm for the minimum cost flow problem on graph-based hypergraphs which are directed hypergraphs of a particular form occurring in railway rotation planning. The algorithm is based on work of Cambini, Gallo, and Scutellà who developed a hypergraphic generalization of the network simplex algorithm, see Cambini et al, Mathematical Programming, 78, 195–217, 1997, [6]. Their main theoretical result is the characterization of basis matrices. We give a similar characterization for graph-based hypergraphs and show that most operations of the simplex algorithm can be done combinatorially by exploiting the underlying digraph structure.

Suggested Citation

  • Isabel Beckenbach, 2018. "A Hypergraph Network Simplex Algorithm," Operations Research Proceedings, in: Natalia Kliewer & Jan Fabian Ehmke & Ralf Borndörfer (ed.), Operations Research Proceedings 2017, pages 309-315, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-89920-6_42
    DOI: 10.1007/978-3-319-89920-6_42
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    Cited by:

    1. Ralf Borndörfer & Thomas Eßer & Patrick Frankenberger & Andreas Huck & Christoph Jobmann & Boris Krostitz & Karsten Kuchenbecker & Kai Mohrhagen & Philipp Nagl & Michael Peterson & Markus Reuther & Th, 2021. "Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization," Interfaces, INFORMS, vol. 51(1), pages 42-62, February.

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