Two New 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 two queries in the adaptive bitprobe model. Previously, the maximum number of elements that can be handled using two queries in the adaptive model is two, which is due to Radhakrishnan et al. [2]. 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 second scheme is to store four elements using four queries in the non-adaptive bitprobe model. The previous scheme to store such a configuration was a non-explicit scheme due to Alon and Fiege [1], and we provide an explicit scheme for the same.