An Improved Scheme in the Two Query Adaptive Bitprobe Model
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^5/6) amount of space. This improves upon the non-explicit scheme proposed by Garg and Radhakrishnan [Garg2015] which uses O(m^16/17) amount of space, and the explicit scheme proposed by Garg [Thesis2015] which uses O(m^14/15) amount of space.
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