Balanced power diagrams for redistricting

TL;DR

This paper introduces a method for redistricting that creates compact, contiguous districts with balanced populations by intersecting convex polygons with the geographical area, optimizing for low dispersion of residents around centers.

Contribution

It presents a novel heuristic algorithm for redistricting that ensures districts are balanced, compact, and contiguous, with polygons having few sides and low dispersion.

Findings

Districts are nearly balanced in population.

Polygons are convex and tend to be compact.

The method minimizes the sum of squared distances to centers.

Abstract

We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the intersection of a polygon with the geographical area. The polygons are convex and the average number of sides per polygon is less than six. The polygons tend to be quite compact. With each polygon is associated a center. The center is the centroid of the locations of the residents associated with the polygon. The algorithm can be viewed as a heuristic for finding centers and a balanced assignment of residents to centers so as to minimize the sum of squared distances of residents to centers; hence the solution can be said to have low dispersion.