Boltzmann Samplers for v-balanced Colored Necklaces

TL;DR

This paper introduces an efficient linear-time Boltzmann sampler for generating v-balanced colored necklaces with constrained bead colors, demonstrating how to handle non-decomposable specifications by mixing sampling methods.

Contribution

It presents the first linear-time Boltzmann sampler for v-balanced necklaces and shows how to combine samplers to handle non-decomposable structures.

Findings

Sampler operates in expected linear time

Effective handling of non-decomposable specifications

Mixing samplers extends applicability of Boltzmann models

Abstract

This paper is devoted to the random generation of particular colored necklaces for which the number of beads of a given color is constrained (these necklaces are called v-balanced). We propose an efficient sampler (its expected time complexity is linear) which satisfies the Boltzmann model principle introduced by Duchon, Flajolet, Louchard and Schaeffer. Our main motivation is to show that the absence of a decomposable specification can be circumvented by mixing the Boltzmann samplers with other types of samplers.