Mathematical Programming

, Volume 78, Issue 2, pp 195–217 | Cite as

Flows on hypergraphs

  • Riccardo Cambini
  • Giorgio Gallo
  • Maria Grazia Scutellà


We consider the capacitated minimum cost flow problem on directed hypergraphs. We define spanning hypertrees so generalizing the spanning tree of a standard graph, and show that, like in the standard and in the generalized minimum cost flow problems, a correspondence exists between bases and spanning hypertrees. Then, we show that, like for the network simplex algorithms for the standard and for the generalized minimum cost flow problems, most of the computations performed at each pivot operation have direct hypergraph interpretations.


Flows Leontief flows Hypergraphs Simplex algorithm 


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Copyright information

© The Mathematical Programming Society, Inc 1997

Authors and Affiliations

  • Riccardo Cambini
    • 1
  • Giorgio Gallo
    • 2
  • Maria Grazia Scutellà
    • 2
  1. 1.Dipartimento di Statistica e Matematica applicata all’EconomiaUniversità di PisaPisaItaly
  2. 2.Dipartimento di InformaticaUniversità di PisaPisaItaly

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