A Hypergraph Network Simplex Algorithm

Please always quote using this URN: urn:nbn:de:0297-zib-64539
  • 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. Their main theoretical result is the characterization of basis matrices. We give a similar characterization for graph-based hypergraphs and show that some operations of the simplex algorithm can be done combinatorially by exploiting the underlying digraph structure.

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Author:Isabel Beckenbach
Document Type:ZIB-Report
Date of first Publication:2017/07/17
Series (Serial Number):ZIB-Report (17-36)