Membership in Constant Time and Almost-Minimum Space

Abstract

This paper deals with the problem of storing a subset of elements from the bounded universe $\mathcal{M} = \{0, \ldots, M-1\}$ so that membership queries can be performed efficiently. In particular, we introduce a data structure to represent a subset of $N$ elements of $\mathcal{M}$ in a number of bits close to the information-theoretic minimum, $B = \left\lceil \lg {M\choose N} \right\rceil$, and use the structure to answer membership queries in constant time.