Improved Bounds for Two Query Adaptive Bitprobe Schemes Storing Five Elements

10/07/2019

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by   Mirza Galib Anwarul Husain Baig, et al.

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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].