Improved Bounds for Two Query Adaptive Bitprobe Schemes Storing Five Elements
Abstract
In this paper, we study two-bitprobe adaptive schemes storing five elements. For these class of schemes, the best known lower bound is m^{1/2} due to Alon and Feige [SODA 2009]. Recently, it was proved by Kesh [FSTTCS 2018] that two-bitprobe adaptive schemes storing three elements will take at least m^{2/3} space, which also puts a lower bound on schemes storing five elements. In this work, we have improved the lower bound to m^{3/4}. We also present a scheme for the same that takes O(m^{5/6}) space. This improves upon the O(m^{18/19})-scheme due to Garg [Ph.D. Thesis] and the O(m^{10/11})-scheme due to Baig et al. [WALCOM 2019].
Cite
@article{arxiv.1910.03651,
title = {Improved Bounds for Two Query Adaptive Bitprobe Schemes Storing Five Elements},
author = {Mirza Galib Anwarul Husain Baig and Deepanjan Kesh},
journal= {arXiv preprint arXiv:1910.03651},
year = {2020}
}
Comments
This paper is accepted in the proceeding of COCOA 2019. arXiv admin note: substantial text overlap with arXiv:1810.13331