Finding Regions of Maximum Circularity in Plane Geometric Graphs
A problem that occurs in different applications in geographical information science is to generate compact regions from areas on a map. This is important, e.g., in the context of electoral districting to avoid gerrymandering. A common measure for the compactness of a region is the Polsby-Popper score, which measures how close a given region is to a circle based on its area and perimeter. We assume that a polygonal subdivision of the plane is given and study the problem of selecting a subset of the polygonal faces that maximizes the Polsby-Popper score.
- Published in:
arXiv - Type:
Article - Authors:
- Year:
2026 - Source:
https://arxiv.org/abs/2607.28298
Citation information
: Finding Regions of Maximum Circularity in Plane Geometric Graphs, arXiv, 2026, July, https://arxiv.org/abs/2607.28298, Haunert.etal.2026a,
@Article{Haunert.etal.2026a,
author={Haunert, Jan-Henrik; Könen, Joshua Marc; Röglin, Heiko; Stuck, Tarek},
title={Finding Regions of Maximum Circularity in Plane Geometric Graphs},
journal={arXiv},
month={July},
url={https://arxiv.org/abs/2607.28298},
year={2026},
abstract={A problem that occurs in different applications in geographical information science is to generate compact regions from areas on a map. This is important, e.g., in the context of electoral districting to avoid gerrymandering. A common measure for the compactness of a region is the Polsby-Popper score, which measures how close a given region is to a circle based on its area and perimeter. We...}}
