Spatio-temporal join selectivity

Given two sets S1, S2 of moving objects, a future timestamp tq, and a distance threshold d, a spatio-temporal join retrieves all pairs of objects that are within distance d at tq. The selectivity of a join equals the number of retrieved pairs divided by the cardinality of the Cartesian product S1×S2. This paper develops a model for spatio-temporal join selectivity estimation based on rigorous probabilistic analysis, and reveals the factors that affect the selectivity. Initially, we solve the problem for 1D (point and rectangle) objects whose location and velocities distribute uniformly, and then extend the results to multi-dimensional spaces. Finally, we deal with non-uniform distributions using a specialized spatio-temporal histogram. Extensive experiments confirm that the proposed formulae are highly accurate (average error below 10%).