Abstract The Doubly Connected Edge List (DCEL) is an edge-list structure widely used in spatial applications, primarily for planar topological and geometric computations. However, it is also applicable to various types of data, including 3D models and geographic data. An essential operation is the overlay operation, which combines the DCELs of two input polygon layers and can easily support spatial queries on polygons like the intersection, union, and difference between these layers. However, existing techniques for spatial overlay operations suffer from two main limitations. First, they fail to handle many large datasets practically used in real applications. Second, they cannot handle arbitrary spatial lines that practically form polygons, e.g., city blocks, but they are given as a set of scattered lines. This work proposes a distributed and scalable way to compute the overlay operation and its related supported queries. Our operations also support arbitrary spatial lines through a scalable polygonization process. We address the issues of efficiently distributing the lines and overlay operators and offer various optimizations that improve performance. Our experiments demonstrate that the proposed scalable solution can efficiently compute the overlay of large real datasets.

The Doubly Connected Edge List (DCEL) is an edge-list structure that has been widely utilized in spatial applications for planar topological computations. An important operation is the overlay which combines the DCELs of two input layers and can easily support spatial queries like the intersection, union and difference between these layers. However, existing sequential implementations for computing the overlay do not scale and fail to complete for large datasets (for example the US census tracks). In this paper we propose a distributed and scalable way to compute the overlay operation and its related supported queries. We address the issues involved in efficiently distributing the overlay operator and offer various optimizations that improve performance. Our scalable solution can compute the overlay of very large real datasets (32M edges) in few minutes.

Recent advances in technology and the widespread use of tracking global positioning systems, such as GPS and RFID, and mobile technologies have made the access to spatio-temporal datasets increase at an accelerated pace. This large amount of data has led to develop efficient techniques to process queries about the behavior of moving objects, like the discovering of patterns among trajectories in a continuous period of time. Several studies have focused on the query of patterns capturing the behavior of moving objects reflected in collaborations such as mobile clusters, convoy queries and flock patterns. In this paper, a comparison between two algorithms for flocking, Basic Flock Evaluation (BFE) and LCMFLOCK, is presented in order to measure their performance and behavior in different datasets, both synthetic and real. This research is the first step towards proposing new algorithms in order to improve the drawbacks reported by the former methods.

The popularity of tracking devices continues to contribute to increasing volumes of spatio-temporal data about moving objects. Current approaches in analysing these data are unable to capture collective behaviour and correlations among moving objects. An example of these types of patterns is moving flocks. This article develops an improved algorithm for mining such patterns following a frequent pattern discovery approach, a well-known task in traditional data mining. It uses transaction-based data representation of trajectories to generate a database that facilitates the application of scalable and efficient frequent pattern mining algorithms. Results were compared with an existing method (Basic Flock Evaluation or BFE) and are demonstrated for both synthetic and real data sets with a large number of trajectories. The results illustrate a significant performance increase. Furthermore, the improved algorithm has been embedded into a visual environment that allows manipulation of input parameters and interactive recomputation of the resulting flocks. To illustrate the visual environment a data set containing 30 years of tropical cyclone tracks with 6 hourly observations is used. The example illustrates how the visual environment facilitates exploration and verification of flocks by changing the input parameters and instantly showing the spatio-temporal distribution of the resulting flocks in the Space-Time Cube and interactively selecting, querying and saving the resulting flocks for further analysis and verification.