Lower Bounds for Restricted Schemes in the Two-Adaptive Bitprobe Model

Abstract: In the adaptive bitprobe model answering membership queries in two bitprobes, we consider the class of restricted schemes as introduced by Kesh and Sharma (Discrete Applied Mathematics 2021). In that paper, the authors showed that such restricted schemes storing subsets of size 2 require $\Omega(m^\frac{2}{3})$ space. In this paper, we generalise the result to arbitrary subsets of size $n$, and prove that the space required for such restricted schemes will be $\Omega(\left(\frac{m}{n}\right)^{1 - \frac{1}{\lfloor n / 4 \rfloor + 2}})$.