Abstract
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 \(\mathcal {O}(m^{5/6})\) amount of space. This improves upon the non-explicit scheme proposed by Garg and Radhakrishnan [5] which uses \(\mathcal {O}(m^{16/17})\) amount of space, and the explicit scheme proposed by Garg [4] which uses \(\mathcal {O}(m^{14/15})\) amount of space. The proposed scheme also answers an open problem posed by Nicholson [8] in the affirmative. Furthermore, we look into a counterexample that shows that our proposed scheme cannot be used to store five or more elements.
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References
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Baig, M.G.A.H., Kesh, D., Sodani, C. (2019). An Improved Scheme in the Two Query Adaptive Bitprobe Model. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_3
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