Algorithms for fundamental spatial aggregate operations over regions

Aggregate operators are a useful class of operators in relational databases. In this paper, we examine spatial aggregate operators over regions. Spatial aggregates are defined to operate over a set of regions, and return a single region as a result. We systematically identify individual spatial aggregate operations by extending existing spatial operations into aggregate form. Semantic meaning for each operator is defined over a specified data model. Once defined, algorithms for computing spatial aggregates over regions are provided. We show that all proposed aggregates can be computed using a single algorithm. Furthermore, we provide serial and parallel algorithm constructions that can take advantage of vector co-processors, such as graphical processing units (GPUs), and that can be integrated into map/reduce queries to take advantage of big data-style clusters. Example queries and their results are provided.