Strongly polynomial algorithm for the intersection of a line with a polymatroid
Résumé
We present a new algorithm for the problem of determining the intersection of a half-line with a polymatroid. We then propose a second algorithm which generalizes the first algorithm and solves a parametric linear program. We prove that these two algorithms are strongly polynomial and that their running time is O ( n 8 + γ n 7 ) where γ is the time for an oracle call. The second algorithm gives a polynomial algorithm to solve the submodular function minimization problem and to compute simultaneously the strength of a network with complexity bound O ( n 8 + γ n 7 ).
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