Space-Time Trade-Offs for Orthogonal Range Queries

Abstract

This paper investigates the question of (storage) space-(retrieval) time trade-off for orthogonal range queries on a static data base. Each record in the data base consists of a key that is a d-tuple of integers, and a data value that is an element in a commutative semigroup G. An orthogonal range query is specified by a d-dimensional parallelepiped (box). Two types of response to such a query are considered: one where the output is the semigroup sum of the data values whose keys are located in the query parallelepiped, and the other where the output is a list of all the records whose keys lie in the query parallelepiped. This paper studies two models, the arithmetic model and the tree model and obtains lower bounds on the product of retrieval time and storage space in both models.