Boltzmann Samplers for Colored Combinatorial Objects

TL;DR

This paper introduces a general framework for Boltzmann sampling of colored combinatorial objects, enabling efficient generation even when classes lack analytic generating functions.

Contribution

It proposes the concept of profiled objects, facilitating sampling of size-colored and k-colored objects in complex combinatorial classes.

Findings

Framework successfully samples a wide range of colored objects.

Profiles enable sampling without explicit generating functions.

Method extends Boltzmann sampling to non-analytic classes.

Abstract

In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored objects (and also of k-colored objects) although the corresponding class cannot be described by an analytic ordinary generating function.