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Approximating the Number of Bases for Almost All Matroids



Brian D. Cloteaux


We define a class of matroids A for which a fully polynomial randomized approximation scheme (fpras) exists for counting the number of bases of the matroids. We then show that as the number of elements in a matroid increases, the probability that a matroid belongs to A goes to 1. We thus provide a fpras for counting the number of bases that applies to almost all matroids.
Congressus Numerantium


matroids, randomized algorithms


Cloteaux, B. (2011), Approximating the Number of Bases for Almost All Matroids, Congressus Numerantium, [online], (Accessed June 23, 2024)


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Created February 1, 2011, Updated February 19, 2017