Hypergraphic submodular function minimization

We generalize the results of Anglès d’Auriac, Iglói, Preissmann and Sebő [1,6] concerning graphic submodular function minimization. They use a subroutine due to Padberg and Wolsey (1983) [5] that cannot be adapted to hypergraphs. Instead of their approach we consider fractional orientations and the push–relabel method Goldberg and Tarjan (1988) [4]. The complexity of the resulting algorithm in a hypergraph is O ( n 4 + n 3 m ) , where n , m are the number of nodes and hyperedges, respectively.