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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Strongly Polynomial Algorithm for the Intersection of a Line with a Polymatroid
verfasst von : Jean Fonlupt, Alexandre Skoda
Erschienen in: Research Trends in Combinatorial Optimization
Verlag: Springer Berlin Heidelberg
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We present a new algorithm for the problem of determining the intersection of a half-line
$\Delta_{u}=\{x\in \mathbb{R}^{N}\:|\:x=\lambda u\;\mathrm {for}\;\lambda \geq 0\}$
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
).