Space Complexity of Two Adaptive Bitprobe Schemes Storing Three Elements

Abstract

We consider the following set membership problem in the bitprobe model - that of storing subsets of size at most three from a universe of size m, and answering membership queries using two adaptive bitprobes. Baig and Kesh [Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2018] proposed a scheme for the problem which takes O(m^{2/3}) space. In this paper, we present a proof which shows that any scheme for the problem requires Omega(m^{2/3}) amount of space. These two results together settle the space complexity issue for this particular problem.