# Constrained clustering via diagrams: A unified theory and its applications to electoral district design

## TL;DR

This paper introduces a unified theoretical framework for constrained clustering using diagrams, demonstrating its efficiency and flexibility through applications to electoral district design with real-world data.

## Contribution

It develops a general, unified theory for constrained clustering based on diagrams, generalizing known results and providing new structural and algorithmic insights.

## Key findings

- Framework is computationally efficient and flexible.
- Successfully applied to electoral district design.
- Demonstrates practical effectiveness on real-world data.

## Abstract

The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and unified) which show that the approach is computationally efficient and flexible enough to pursue various conflicting demands. The strength of the model is also demonstrated practically on real-world instances of the electoral district design problem where municipalities of a state have to be grouped into districts of nearly equal population while obeying certain politically motivated requirements.