Two remarks concerning balanced matroids
Combinatorics
2007-05-23 v1
Abstract
The property of balance (in the sense of Feder and Mihail) is investigated in the context of paving matroids. The following examples are exhibited: (a) a class of ``sparse'' paving matroids that are balanced, but at the same time rich enough combinatorially to permit the encoding of hard counting problems; and (b) a paving matroid that is not balanced. The computational significance of (a) is the following. As a consequence of balance, there is an efficient algorithm for approximating the number of bases of a sparse paving matroid within specified relative error. On the other hand, determining the number of bases exactly is likely to be computationally intractable.
Cite
@article{arxiv.math/0404200,
title = {Two remarks concerning balanced matroids},
author = {Mark Jerrum},
journal= {arXiv preprint arXiv:math/0404200},
year = {2007}
}