Sampling-based techniques for designing school boundaries

TL;DR

This paper introduces sampling-based techniques for designing school boundaries, inspired by redistricting methods, to serve as baselines and to analyze problem characteristics for improved algorithms.

Contribution

It adapts flip proposal sampling techniques from political redistricting to school boundary design, providing tools for comparison and problem analysis.

Findings

Sampling techniques can serve as baselines for school boundary algorithms.

They help infer characteristics of the school redistricting problem.

Empirical analysis demonstrates their utility in practice.

Abstract

Recently, an increasing number of researchers, especially in the realm of political redistricting, have proposed sampling-based techniques to generate a subset of plans from the vast space of districting plans. These techniques have been increasingly adopted by U.S. courts of law and independent commissions as a tool for identifying partisan gerrymanders. Motivated by these recent developments, we develop a set of similar sampling techniques for designing school boundaries based on the flip proposal. Note that the flip proposal here refers to the change in the districting plan by a single assignment. These sampling-based techniques serve a dual purpose. They can be used as a baseline for comparing redistricting algorithms based on local search. Additionally, these techniques can help to infer the problem characteristics that may be further used for developing efficient redistricting methods. We empirically touch on both these aspects in regards to the problem of school redistricting.