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 -representation, given their representation in terms of Minkowski sum of known segments.
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}
}