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The widespread availability of geotagged data combined with modern map services allows for the accurate attachment of data to spatial networks. Applying statistical analysis, such as hotspot detection, over spatial networks is very important for precise quantification and patterns analysis, which empowers effective decision-making in various important applications. Existing hotspot detection algorithms on spatial networks either lack sufficient statistical evidence on detected hotspots, such as clustering, or they provide statistical evidence at a prohibitive computational overhead. In this paper, we propose efficient algorithms for detecting hotspots based on the network local K-function for predefined and unknown hotspot radii. The K-function is a widely adopted statistical approach for network pattern analysis that enables the understanding of the density and distribution of activities and events happening within the spatial network. However, its practical application has been limited due to the inefficiency of state-of-the-art algorithms, particularly for large-sized networks. Extensive experimental evaluation using real and synthetic datasets shows that our algorithms are up to 28 times faster than the state-of-the-art algorithms in computing hotspots with a predefined radius and up to more than four orders of magnitude faster in identifying hotspots without a predefined radius. Additionally, to address dynamic changes in the spatial network, we propose an incremental hotspot detection approach that efficiently updates hotspot computations by leveraging prior results as new events are added. 

Social media platforms generate massive amounts of data that reveal valuable insights about users and communities at large. Existing techniques have not fully exploited such data to help practitioners perform a deep analysis of large online communities. Lack of scalability hinders analyzing communities of large sizes and requires tremendous system resources and unacceptable runtime. This article proposes a new analytical query that identifies the top-kposts that a given user community has interacted with during a specific time interval and within a spatial range. We propose a novel indexing framework that captures the interactions of users and communities to provide a low query latency. Moreover, we propose exact and approximate algorithms to process the query efficiently and utilize the index content to prune the search space. The extensive experimental evaluation on real data has shown the superiority of our techniques and their scalability to support large online communities. 

The widespread of geotagged data combined with modern map services allows for the accurate attachment of data to spatial networks. Applying statistical analysis, such as hotspot detection, over spatial networks is very important for precise quantification and patterns analysis, which empowers effective decision-making in various important applications. Existing hotspot detection algorithms on spatial networks either lack statistical evidence on detected hotspots, such as clustering, or they provide statistical evidence at a prohibitive computational overhead. In this paper, we propose efficient algorithms for detecting hotspots based on the network local K-function for predefined and unknown hotspot radii. The network local K-function is a widely adopted statistical approach for network pattern analysis that enables the understanding of the density and distribution of activities and events in the spatial network. However, its practical application has been limited due to the inefficiency of existing algorithms, particularly for large-sized networks. Extensive experimental evaluation using real and synthetic datasets shows that our algorithms are up to 28 times faster than the state-of-the-art algorithms in computing hotspots with a predefined radius and up to more than four orders of magnitude faster in identifying hotspots without a predefined radius. 

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. 

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.