Bonsai: A class of effective methods for independent sampling of graph partitions

TL;DR

This paper introduces a new class of methods called Bonsai for independently sampling graph partitions, offering an alternative to Markov Chain algorithms, with applications to districting and legislative maps.

Contribution

The paper presents Bonsai, a novel approach for independent sampling of graph partitions, including explicit distributions for balanced districts, improving over traditional Markov Chain methods.

Findings

Bonsai performs comparably or better than Markov Chain algorithms in experiments.

The method provides explicit sampling distributions for perfectly balanced districts.

Applications demonstrated on grid graphs and legislative maps.

Abstract

We develop effective methods for constructing an ensemble of district plans via independent sampling from a reasonable probability distribution on the space of graph partitions. We compare the performance of our algorithms to that of standard Markov Chain based algorithms in the context of grid graphs and state congressional and legislative maps. For the case of perfect population balance between districts, we provide an explicit description of the distribution from which our method samples.