Boltzmann Sampling of Unlabelled Structures

Philippe Flajolet (1) , Eric Fusy (1) , Carine Pivoteau (1, 2)

1 ALGORITHMS - Algorithms
2 APR - Algorithmes, Programmes et Résolution

Boltzmann models from statistical physics, combined with methods from analytic combinatorics, give rise to efficient algorithms for the random generation of unlabelled objects. The resulting algorithms generate in an unbiased manner discrete configurations that may have nontrivial symmetries, and they do so by means of real-arithmetic computations. Here you'll find a collection of construction rules for such samplers, which applies to a wide variety of combinatorial classes, including integer partitions, necklaces, unlabelled functional graphs, dictionaries, series-parallel circuits, term trees and acyclic molecules obeying a variety of constraints.

Mots clés: Boltzmann samplers; Random sampling; Analytic combinatorics

Domaines: Combinatoire [math.CO]

Philippe Flajolet, Eric Fusy, Carine Pivoteau. Boltzmann Sampling of Unlabelled Structures. Workshop on Analytic Algorithmics and Combinatorics, Jan 2007, New Orleans, United States. pp.201-211, ⟨10.1137/1.9781611972979.5⟩. ⟨hal-00782866⟩