A Hypergraph Network Simplex Algorithm

Isabel Beckenbach ()
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Isabel Beckenbach: Zuse Institute Berlin

A chapter in Operations Research Proceedings 2017, 2018, pp 309-315 from Springer

Abstract: 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.

Keywords: Directed hypergraphs; Min-cost flow; Network simplex (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-89920-6_42

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