Spatial Regionalization: Algorithms and Challenges

Spatial regionalization seeks to partition a set of spatial polygons into contiguous, non-overlapping regions that optimize a specified objective function.This problem is fundamental in diverse applications across environmental science, urban planning, and public health, serving purposes such as resource allocation, policy formulation, and disease monitoring.Due to its computational complexity as an NP-hard problem, researchers typically rely on heuristics and approximation algorithms to achieve a practical balance between accuracy and runtime efficiency.This tutorial comprehensively reviews the main methodologies in the field, systematically categorizing them into three primary groups: (i) exact algorithms, (ii) top-down divisive strategies, and (iii) bottom-up agglomerative techniques.We detail each category by highlighting the core principles and representative algorithms.Furthermore, we identify and discuss open challenges in spatial regionalization.