Abstract
In the adaptive bitprobe model, consider the following set membership problem – store subsets of size at most two from an universe of size m, and answer membership queries using two bitprobes. Radhakrishnan et al. [3] proposed a scheme for the problem which takes \(\mathcal {O}(m^{2/3})\) amount of space, and conjectured that this is also the lower bound for the problem. We propose a proof of the lower bound for the problem, but for a restricted class of schemes. This proof hopefully makes progress over the ideas proposed by Radhakrishnan et al. [3] and [4] towards the conjecture.
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References
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Acknowledgement
The authors would like to thank Protyai Ghosal for useful insights and discussions throughout the duration of the work.
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Kesh, D., Sharma, V.S. (2019). On the Bitprobe Complexity of Two Probe Adaptive Schemes Storing Two Elements. In: Pal, S., Vijayakumar, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science(), vol 11394. Springer, Cham. https://doi.org/10.1007/978-3-030-11509-8_5
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DOI: https://doi.org/10.1007/978-3-030-11509-8_5
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