Analyzing Boltzmann Samplers for Bose–Einstein Condensates with Dirichlet Generating Functions

Bernstein, Megan; Fahrbach, Matthew; Randall, Dana

doi:10.1137/1.9781611975062.10

Cited by 2 publications

(1 citation statement)

References 17 publications

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“…In his article [Ver96], Vershik considers several combinatorial examples related to statistical mechanics and obtains the limit shape for a random integer partition of size n with α √ n parts and summands bounded by θ √ n. Let us remark that Bernstein, Fahrbach, and Randall [BFR18] have recently analysed the complexity of exact-size Boltzmann sampler for weighted partitions. In the model of ideal gas, there are several particles (bosons) which form a so-called assembly of particles.…”

Section: Applicationsmentioning

confidence: 99%

Polynomial tuning of multiparametric combinatorial samplers

Bendkowski¹,

Bodini²,

Dovgal³

2018

2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various treelike structures. In their multiparametric variants, these samplers allow to control the profile of expected values corresponding to multiple combinatorial parameters. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain subpatterns in strings. However, such a flexible control requires an additional nontrivial tuning procedure. In this paper, we propose an efficient polynomial-time, with respect to the number of tuned parameters, tuning algorithm based on convex optimisation techniques. Finally, we illustrate the efficiency of our approach using several applications of rational, algebraic and Pólya structures including polyomino tilings with prescribed tile frequencies, planar trees with a given specific node degree distribution, and weighted partitions.

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Section: Applicationsmentioning

confidence: 99%

Polynomial tuning of multiparametric combinatorial samplers

Bendkowski¹,

Bodini²,

Dovgal³

2018

2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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Tuning as convex optimisation: a polynomial tuner for multi-parametric combinatorial samplers

Bendkowski

Bodini

Dovgal

2021

Combinator. Probab. Comp.

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Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules. They can be adapted to combinatorial specifications with additional parameters, allowing for a more flexible control over the output profile of parametrised combinatorial patterns. One can control, for instance, the number of leaves, profile of node degrees in trees or the number of certain sub-patterns in generated strings. However, such a flexible control requires an additional and nontrivial tuning procedure. Using techniques of convex optimisation, we present an efficient tuning algorithm for multi-parametric combinatorial specifications. Our algorithm works in polynomial time in the system description length, the number of tuning parameters, the number of combinatorial classes in the specification, and the logarithm of the total target size. We demonstrate the effectiveness of our method on a series of practical examples, including rational, algebraic, and so-called Pólya specifications. We show how our method can be adapted to a broad range of less typical combinatorial constructions, including symmetric polynomials, labelled sets and cycles with cardinality lower bounds, simple increasing trees or substitutions. Finally, we discuss some practical aspects of our prototype tuner implementation and provide its benchmark results.

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Analyzing Boltzmann Samplers for Bose–Einstein Condensates with Dirichlet Generating Functions

Cited by 2 publications

References 17 publications

Polynomial tuning of multiparametric combinatorial samplers

Polynomial tuning of multiparametric combinatorial samplers

Tuning as convex optimisation: a polynomial tuner for multi-parametric combinatorial samplers

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