Average-Case Analysis for a Simple Compression Algorithm

Abstract.

In this paper we treat the static dictionary problem , very well known in computer science. It consists in storing a set S of m elements in the range [1 . . . n ] so that membership queries on S 's elements can be handled in O(1) time. It can be approached as a table compression problem in which a size n table has m ones and the other elements are zeros. We focus our attention on sparse case (m $\ll$ n ). We use a simple algorithm to solve the problem and make an average-case analysis of the total space required when the input derives from uniform probability distribution. We also find some conditions able to minimize storage requirements. We then propose and analyze a new algorithm able to reduce storage requirements drastically to O(m ^4/3 ) .