Two improved schemes in the bitprobe model

Abstract

In this paper, we describe two new explicit schemes in the bitprobe model that, to the best of our knowledge, improves upon the existing schemes in the literature. One such scheme is to store three elements using O(m2/3) amount of space and answer membership queries using two adaptive bitprobes. Previously, the maximum number of elements that could be handled using two queries and O(m2/3) amount of space is two, which is due to Radhakrishnan et al. [1]. A corollary of this result is an explicit scheme for storing three elements using three queries in the non-adaptive model, a first such scheme in the model. The next scheme uses four bitprobes in the non-adaptive bitprobe model and uses O(m2/3) amount of space to accommodate five elements using the block-superblock idea of Radhakrishnan et al. [1]. The previous scheme to store such a configuration was a non-explicit scheme due to Alon and Fiege [2], and we provide an explicit scheme for the same.