English

Output-sensitive algorithm for generating the flats of a matroid

Combinatorics 2011-07-22 v1

Abstract

We present an output-sensitive algorithm for generating the whole set of flats of a finite matroid. Given a procedure, P, that decides in S_P time steps if a set is independent, the time complexity of the algorithm is O(N^2 M S_P), where N and M are the input and output size, respectively. In the case of vectorial matroids, a specific algorithm is reported whose time complexity is equal to O(N^2 M d^2), d being the rank of the matroid. In some cases this algorithm can provide an efficient method for computing zonotopes in HH-representation, given their representation in terms of Minkowski sum of known segments.

Keywords

Cite

@article{arxiv.1107.4301,
  title  = {Output-sensitive algorithm for generating the flats of a matroid},
  author = {A. Montina},
  journal= {arXiv preprint arXiv:1107.4301},
  year   = {2011}
}
R2 v1 2026-06-21T18:40:07.832Z