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This paper introduces a generalized spatial regionalization problem, namely, PRUC ( P -Regions with User-defined Constraint) that partitions spatial areas into homogeneous regions. PRUC accounts for user-defined constraints imposed over aggregate region properties. We show that PRUC is an NP-Hard problem. To solve PRUC, we introduce GSLO (Global Search with Local Optimization), a parallel stochastic regionalization algorithm. GSLO is composed of two phases: (1) Global Search that initially partitions areas into regions that satisfy a user-defined constraint, and (2) Local Optimization that further improves the quality of the partitioning with respect to intra-region similarity. We conduct an extensive experimental study using real datasets to evaluate the performance of GSLO. Experimental results show that GSLO is up to 100× faster than the state-of-the-art algorithms. GSLO provides partitioning that is up to 6× better with respect to intra-region similarity. Furthermore, GSLO is able to handle 4× larger datasets than the state-of-the-art algorithms. 

The proliferation of GPS-enabled devices has led to the development of numerous location-based services. These services need to process massive amounts of streamed spatial data in real-time. The current scale of spatial data cannot be handled using centralized systems. This has led to the development of distributed spatial streaming systems. Existing systems are using static spatial partitioning to distribute the workload. In contrast, the real-time streamed spatial data follows non-uniform spatial distributions that are continuously changing over time. Distributed spatial streaming systems need to react to the changes in the distribution of spatial data and queries. This article introduces SWARM, a lightweight adaptivity protocol that continuously monitors the data and query workloads across the distributed processes of the spatial data streaming system and redistributes and rebalances the workloads as soon as performance bottlenecks get detected. SWARM is able to handle multiple query-execution and data-persistence models. A distributed streaming system can directly use SWARM to adaptively rebalance the system’s workload among its machines with minimal changes to the original code of the underlying spatial application. Extensive experimental evaluation using real and synthetic datasets illustrate that, on average, SWARM achieves 2 improvement in throughput over a static grid partitioning that is determined based on observing a limited history of the data and query workloads. Moreover, SWARM reduces execution latency on average 4 compared with the other technique.