18 Multidimensional Data Structures

The representation of multidimensional data is an important issue in applications in diverse fields that include database management systems, computer graphics, computer vision, computational geometry, image processing, geographic information systems (GIS), pattern recognition, VLSI design, and others. The most common definition of multidimensional data is a collection of points in a higher dimensional space. These points can represent locations and objects in space as well as more general records. As an exampleof a record, consider an employee record that has attributes corresponding to the employee’s name, address, sex, age, height, weight, and social security number. Such records arise in database management systems and can be treated as points in, for this example, a seven-dimensional space (i.e., there is one dimension for each attribute), albeit the different dimensions have different type units (i.e., name and address are strings of characters, sex is binary; while age, height, weight, and social security number are numbers). Whenmultidimensional data corresponds to locational data, we have the additional property that all of the attributes have the same unit, which is distance in space. In this case, we can combine the attributes and pose queries that involve proximity. For example, we may wish to find the closest city to Chicago within the two-dimensional space fromwhich the locations of the cities are drawn. Another query seeks to find all cities within 50miles of Chicago. In contrast, such queries are not very meaningful when the attributes do not have the same type. For example, it is not customary to seek the person with age–weight combination closest to John Jones, as we do not have a commonly accepted unit of year-pounds (year-kilograms) or