Orthogonal Range Searching

Abstract

At first sight it seems that databases have little to do with geometry. Nevertheless, many types of questions—from now on called queries—about data in a database can be interpreted geometrically. To this end we transform records in a database into points in a multi-dimensional space, and we transform the queries about the records into queries on this set of points. Let's demonstrate this with an example. Interpreting a database query geometrically Consider a database for personnel administration. In such a database the name, address, date of birth, salary, and so on, of each employee are stored. A typical query one may want to perform is to report all employees born between 1950 and 1955 who earn between $3,000 and $4,000 a month. To formulate this as a geometric problem we represent each employee by a point in the plane. The first coordinate of the point is the date of birth, represented by the integer 10, 000 × year + 100 × month + day, and the second coordinate is the monthly salary. With the point we also store the other information we have about the employee, such as name and address. The database query asking for all employees born between 1950 and 1955 who earn between $3,000 and 95