A new algorithm for the intersection of a line with the independent set polytope of a matroid

Alexandre Skoda (1)

1 CES - Centre d'économie de la Sorbonne

We present a new algorithm for the problem of determining the intersection of a half-line Δu = {x | x = λu, λ ≥ 0, u ∈ Rn+} with the independent set polytope of a matroid. We show it can also be used to compute the strength of a graph and the corresponding partition using successive contractions. The algorithm is based on the maximization of successive linear forms on the boundary of the polytope. We prove it is a polynomial algorithm in probability with average number of iterations in O(n5). Finally, numerical tests reveal that it should only require O(n2) iterations in practice.

Mots clés: Algorithm; Graph; Strength of a graph; Submodular function; Matroid

Domaines: Recherche opérationnelle [math.OC]; Mathématique discrète [cs.DM]

Alexandre Skoda. A new algorithm for the intersection of a line with the independent set polytope of a matroid. Bulletin des Sciences Mathématiques, 2009, 133 (2), pp.169-185. ⟨hal-00633952⟩