 
Summary: SPACE PARTITIONING AND ITS APPLICATION
TO GENERALIZED RETRIEVAL PROBLEMS
David Avis
School of Computer Science
McGill University
805 Sherbrooke Street West
Montreal, Quebec, Canada H3A 2K6
1. Introduction
A fundamental problem in the area of database systems is the retrieval of data satis
fying 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[10]. A more
difficult problem is the retrieval of data based on criteria for several keys, the socalled
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.
In this paper we study the multidimensional search problem from a geometric stand
point. We consider the d  tuple of keys for a given record as a point in ddimensional
space, R d . The previously mentioned orthogonal range query problem can now be inter
preted as finding all points in a given d  dimensional hyperrectangle. Suppose we are
