On The Complexity Of Some Multi-Attribute File Design-Problems

In this paper, we consider the complexity of two multi-attribute file design problems. We shall first show that the general problem of designing a multi-attribute file system which is optimal with respect to partial match queries is an NP-hard problem. We shall also show that the Cartesian product file design problem is related to the Composite Number Problem. If the Cartesian product file design problem can be solved by a polynomial algorithm, then the Composite Number Problem can also be solved in polynomial time, which is quite unlikely.