Optimizing Districting Plans to Maximize Majority-Minority Districts via IPs and Local Search

In redistricting litigation, effective enforcement of the Voting Rights Act has often involved providing the court with districting plans that display a larger number of majority-minority districts than the current proposal (as was true, for example, in what followed Allen v. Milligan concerning the congressional districting plan for Alabama in 2023). Recent work by Cannon et al. proposed a heuristic algorithm for generating plans to optimize majority-minority districts, which they called short bursts; that algorithm relies on a sophisticated random walk over the space of all plans, transitioning in bursts, where the initial plan for each burst is the most successful plan from the previous burst. We propose a method based on integer programming, where we build upon another previous work, the stochastic hierarchical partitioning algorithm, which heuristically generates a robust set of potential districts (viewed as columns in a standard set partitioning formulation); that approach was designed to optimize a different notion of fairness across a statewide plan. We design a new column generation algorithm to find plans via integer programming that outperforms short bursts on multiple data sets in generating statewide plans with significantly more majority-minority districts. These results also rely on a new local re-optimization algorithm to iteratively improve on any baseline solution, as well as an algorithm to increase the compactness of districts in plans generated (without impacting the number of majority-minority districts).

Scheduling with Predictions

There is significant interest in deploying machine learning algorithms for diagnostic radiology, as modern learning techniques have made it possible to detect abnormalities in medical images within minutes. While machine-assisted diagnoses cannot yet reliably replace human reviews of images by a radiologist, they could inform prioritization rules for determining the order by which to review patient cases so that patients with time-sensitive conditions could benefit from early intervention. We study this scenario by formulating it as a learning-augmented online scheduling problem. We are given information about each arriving patient's urgency level in advance, but these predictions are inevitably error-prone. In this formulation, we face the challenges of decision making under imperfect information, and of responding dynamically to prediction error as we observe better data in real-time. We propose a simple online policy and show that this policy is in fact the best possible in certain stylized settings. We also demonstrate that our policy achieves the two desiderata of online algorithms with predictions: consistency (performance improvement with prediction accuracy) and robustness (protection against the worst case). We complement our theoretical findings with empirical evaluations of the policy under settings that more accurately reflect clinical scenarios in the real world.