Space Partitioning and its Application to Generalized Retrieval Problems

A fundamental problem In the area of database systems Is the retrieval of data satisfying certain criteria. The simplest such problem Is the retrieval of data based on a single key, and a comprehensive treatment of this problem Is contained In Knuth[1]. A more difficult problem Is the retrieval of data based on criteria for several keys, the so-called multidimensional search problem. Suppose that each of n records of a file contains a fixed number, d , of keys. A query asks for all records for which the d keys satisfy certain criteria. For example, upper and lower bounds maybe specified for some or all keys, yielding the socalled orthogonal range query problem.

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