On Connectivity of Efficient Matroid Bases

Abstract

Let M = (N,I) be a matroid. With each element j ∈ N we associate a weight-vector ω(j) ∈ IR ^Q₊ , Q ≥ 2. If S ⊆ N, the weight of S is defined as the vector with components ∑ _{j ∈ S} ω _q (j). A basis B of M is called efficient basis if there is no basis B′ such that ω(B′) < ω(B), i.e. if its corresponding weight-vector is vectorminimal. The multicriteria matroid optimization problem is the following:

(MCMOP) Find all efficient bases of M.

Partially supported by the Deutsche Forschungsgemeinschaft