Lecture Notes: R-trees

In theoretical studies, we often develop structures that are dedicated to specific problems. In practice, often it is unrealistic to create many different indexes on the same dataset to support various types of queries, because doing so will incur prohibitive space consumption and update overhead. Therefore, it would be nice to have a single, all-around, structure, which occupies small space, can be updated efficiently, and most importantly, supports a large variety of queries. In this lecture, we will discuss such an all-around structure called the R-tree. This structure is heuristic in nature, because it does not have any attractive theoretical guarantees on the search performance. Nevertheless, the practical efficiency of this structure has been widely established for many problems, especially if the dimensionality is low. Interestingly, for realistic datasets, there has been evidence [1] that R-trees even outperform some theoretical worst-case efficient structures. This is not as surprising as it may appear. The design of a theoretical structure aims at handling the most adverse datasets. Much of the design is not really needed for “good” datasets, and thus, may actually cause unnecessary overhead on such data. Because of its superb efficiency, the R-tree has become the de facto structure for multi-dimensional indexing in database systems nowadays.