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IJAC
2008

Random Generation of Finitely Generated Subgroups of a Free Group

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Random Generation of Finitely Generated Subgroups of a Free Group
We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be obtained by the method of Stallings foldings. Our algorithm randomly generates a subgroup of a given size n, according to the uniform distribution over size n subgroups. In the process, we give estimates of the number of size n subgroups, of the average rank of size n subgroups, and of the proportion of such subgroups that have finite index. Our algorithm has average case complexity O(n) in the RAM model and O(n2 log2 n) in the bitcost model.
Frédérique Bassino, Cyril Nicaud, Pa
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2008
Where IJAC
Authors Frédérique Bassino, Cyril Nicaud, Pascal Weil
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