2,229 research outputs found
Infinite Boltzmann Samplers and Applications to Branching Processes
National audienceIn this short note, we extend the Boltzmann model for combinatorial random sampling [8] to allow for infinite size objects; in particular, this extension now fully includes Galton-Watson processes. We then illustrate our idea with two examples, one of which is the generation of prefixes of infinite Cayley trees
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(n^2\log^2n) in the bitcost
model
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