External Memory Geometric Data Structures

Many modern applications store and process datasets much larger than the main memory of even state-of-the-art high-end machines. Thus massive and dynamically changing datasets often need to be stored in space efficient data structures on external storage devices such as disks. In such cases the Input/Output (or I/O) communication between internal and external memory can become a major performance bottleneck. Many massive dataset applications involve geometric data (for example points, lines, and polygons) or data that can be interpreted geometrically. Such applications often perform queries that correspond to searching in massive multidimensional geometric databases for objects that satisfy certain spatial constraints. Typical queries include reporting the objects intersecting a query region, reporting the objects containing a query point, and reporting objects near a query point. While development of practically efficient (and ideally also multi-purpose) external memory data structures (or indexes) has always been a main concern in the database community, most data structure research in the algorithms community has focused on worst-case efficient internal memory data structures. Recently however, there has been some cross-fertilization between the two areas. In these lecture notes we discuss some of the recent advances in the development of worstcase efficient external memory geometric data structures. We will focus on fundamental dynamic structures for oneand two-dimensional orthogonal range searching, and try to highlight some of the fundamental techniques used to develop such structures. Accurately modeling memory and disk systems is a complex task. The primary feature of disks we want to model is their extremely long access time relative to that of internal memory. In order to amortize the access time over a large amount of data, typical disks read or write large blocks of contiguous data at once and therefore the standard two-level disk model has the following parameters: