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arXiv · 2510.09334

Optimizing Administrative Divisions: A Vertex $k$-Center Approach for Edge-Weighted Road Graphs

Peteris Daugulis
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Abstract

Efficient and equitable access to municipal services hinges on well-designed administrative divisions. It requires ongoing adaptation to changing demographics, infrastructure, and economic factors. This article proposes a novel transparent data-driven method for territorial division based on the Voronoi partition of edge-weighted road graphs and the vertex $k$-center problem as a special case of the minimax facility location problem. By considering road network structure and strategic placement of administrative centers, this method seeks to minimize travel time disparities and ensure a more balanced distribution of administrative time burden for the population. We show implementations of this approach in the context of Latvia, a country with complex geographical features and diverse population distribution.

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Peteris Daugulis. 2025-10-10. Optimizing Administrative Divisions: A Vertex $k$-Center Approach for Edge-Weighted Road Graphs. https://doi.org/10.22364/bjmc.2024.12.2.04

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