Storing four elements in the two query bitprobe model

Abstract

In this paper, we look into the adaptive bitprobe model that stores subsets of size at most four from a universe of size m , and answers membership queries using two bitprobes. We propose a scheme that stores arbitrary subsets of size four using O ( m 4 / 5 ) amount of space. This improves upon the O ( m 5 / 6 ) -scheme by the authors Baig et al. (2019). The proposed scheme also answers an open problem posed by Nicholson (2019) in the affirmative.