Some properties of optimal Cartesian product files for orthogonal range queries

Abstract

Cartesian product file (CPF) has bren proposed as a good multi-attribute file structure. Although designing an optimal CPF for partial match queries (PMQs) has been proven to be NP-hard, some useful properties have been studied for PMQs to help the work. However, a good CPF for PMQs may not be beneficial for orthogonal range queries (ORQs). Therefore, in this paper, we intend to study properties that help the design of a good CPF for ORQs. We found that the problem of designing the optimal CPF for ORQs is related to the problem of finding a minimal-f N-tuple. We will also show some theories of minimal-f N-tuples and develop a method for generating a minimal-f N-tuple. Finally, we will present some properties of the optimal CPF for ORQs from the theories of minimal-f N-tuples.