Euler++: Improved Selectivity Estimation for Rectangular Spatial Records

Selectivity estimation is one of the common research problems for big spatial data, where the objective is to quickly estimate the number of records in a given query range. Euler histogram has been used to answer the selectivity estimation queries for objects with extents such as rectangles in constant time. However, it is only accurate when the query range is aligned with the histogram grid lines. In this paper, we improve the Euler histogram to accurately answer arbitrary queries, i.e., even if they do not align with the histogram grid lines. The improved histogram, called Euler++, has the same space and time complexity as the regular Euler histogram and provides a better accuracy for objects with extents. We use both real and synthetic datasets for extensive experiments, and show that the proposed technique, Euler++, consistently outperforms the existing ones, while still providing answer in constant time.