Boltzmann sampling of ordered structures

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 a Boltzmann sampler for ordered structures constructed with the box operator, which is an extension of the cartesian product. Under an abstract real-arithmetic computation model, our algorithm is of linear complexity for free generation. For generation of objects of a targetted size, provided a small tolerance, the complexity remains linear for many classes of structures. As an illustration we show how to generate alternating permutations, and our implementation makes possible to generate random objects of sizes up to $10^7$ on a standard machine