Boltzmann sampling of ordered structures

Olivier Roussel 1 Michèle Soria 1
1 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : Boltzmann models from statistical physics combined with methods from analytic combinatorics give rise to efficient algorithms for the random generation of combinatorials objects. This paper proposes an efficient sampler which satisfies the Boltzmann model principle for ordered structures. This goal is achieved using a special operator, named 'box operator'. Under an abstract real-arithmetic computation model, our algorithm is of linear complexity upon free generation ; and for many classical structures, of linear complexity also provided a small tolerance is allowed on the size of the object drawn. The resulting programs make it possible to generate random objects of sizes up to $10^7$ on a standard machine.
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LAGOS 2009 - 5th Latin-American Algorithms, Graphs and Optimization Symposium, Nov 2009, Rio Grande do Sul, Brazil. Elsevier, 35, pp.305-310, 2009, Electronic Notes in Discrete Mathematics. 〈10.1016/j.endm.2009.11.050〉
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Olivier Roussel, Michèle Soria. Boltzmann sampling of ordered structures. LAGOS 2009 - 5th Latin-American Algorithms, Graphs and Optimization Symposium, Nov 2009, Rio Grande do Sul, Brazil. Elsevier, 35, pp.305-310, 2009, Electronic Notes in Discrete Mathematics. 〈10.1016/j.endm.2009.11.050〉. 〈hal-00411110〉

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