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The process of regionalization involves clustering a set of spatial areas into spatially contiguous regions. Given the NP-hard nature of regionalization problems, all existing algorithms yield approximate solutions. To ascertain the quality of these approximations, it is crucial for domain experts to obtain statistically significant evidence on optimizing the objective function, in comparison to a random reference distribution derived from all potential sample solutions. In this paper, we propose a novel spatial regionalization problem, denoted as SISR (Statistical Inference for Spatial Regionalization), which generates random sample solutions with a predetermined region cardinality. The driving motivation behind SISR is to conduct statistical inference on any given regionalization scheme. To address SISR, we present a parallel technique named PRRP (P-Regionalization through Recursive Partitioning). PRRP operates over three phases: the region-growing phase constructs initial regions with a predetermined region cardinality, while the region merging and region-splitting phases ensure the spatial contiguity of unassigned areas, allowing for the growth of subsequent regions with predetermined cardinalities. An extensive evaluation shows the effectiveness of PRRP using various real datasets. 

Regionalization techniques group spatial areas into a set of homogeneous regions to analyze and draw conclusions about spatial phenomena. A recent regionalization problem, called MP-regions, groups spatial areas to produce a maximum number of regions by enforcing a user-defined constraint at the regional level. The MP-regions problem is NP-hard. Existing approximate algorithms for MP-regions do not scale for large datasets due to their high computational cost and inherently centralized approaches to process data. This article introduces a parallel scalable regionalization framework (PAGE) to support MP-regions on large datasets. The proposed framework works in two stages. The first stage finds an initial solution through randomized search, and the second stage improves this solution through efficient heuristic search. To build an initial solution efficiently, we extend traditional spatial partitioning techniques to enable parallelized region building without violating the spatial constraints. Furthermore, we optimize the region building efficiency and quality by tuning the randomized area selection to trade off runtime with region homogeneity. The experimental evaluation shows the superiority of our framework to support an order of magnitude larger datasets efficiently compared to the state-of-the-art techniques while producing high-quality solutions. 

Spatial regionalization is the process of combining a collection of spatial polygons into contiguous regions that satisfy user-defined criteria and objectives. Numerous techniques for spatial regionalization have been proposed in the literature, which employs varying methods for region growing, seeding, optimization, and enforce different user-defined constraints and objectives. This paper introduces a scalable unified system for addressing seeding spatial regionalization queries efficiently. The proposed system provides a usable and scalable framework that employs a wide-range of existing spatial regionalization techniques and allows users to submit novel combinations of queries that have not been previously explored. This represents a significant step forward in the field of spatial regionalization as it provides a robust platform for addressing different regionalization queries. The system is mainly composed of three components: query parser, query planner, and query executor. Preliminary evaluations of the system demonstrate its efficacy in efficiently addressing various regionalization queries.