Improvements to exact Boltzmann sampling using probabilistic divide-and-conquer and the recursive method

TL;DR

This paper introduces an improved exact sampling method for discrete distributions by combining Boltzmann sampling, the recursive method, and probabilistic divide-and-conquer, broadening applicability and efficiency.

Contribution

It presents a hybrid approach that integrates Boltzmann sampling with probabilistic divide-and-conquer, enabling exact sampling for a wide class of combinatorial distributions.

Findings

Method generalizes to various combinatorial distributions

Explicit examples demonstrate broad applicability

Achieves exact sampling with improved efficiency

Abstract

We demonstrate an approach for exact sampling of certain discrete combinatorial distributions, which is a hybrid of exact Boltzmann sampling and the recursive method, using probabilistic divide-and-conquer (PDC). The approach specializes to exact Boltzmann sampling in the trivial setting, and specializes to PDC deterministic second half in the first non-trivial application. A large class of examples is given for which this method broadly applies, and several examples are worked out explicitly.