Abstract
Buhrman et al. [SICOMP 2002] studied the membership problem in the bitprobe model, presenting both randomized and deterministic schemes for storing a set of size n from a universe of size m such that membership queries on the set can be answered using t bit probes. Since then, there have been several papers focusing on deterministic schemes, especially for the first non-trivial case when n = 2. The most recent, due to Radhakrishnan, Shah, and Shannigrahi [ESA 2010], describes non-explicit schemes (existential results) for t ≥ 3 using probabilistic arguments. We describe a fully explicit scheme for n = 2 that matches their space bound of Θ(m 2/5) bits for t = 3 and, furthermore, improves upon it for t > 3, answering their open problem. Our structure (consisting of query and storage algorithms) manipulates blocks of bits of the query element in a novel way that may be of independent interest. We also describe recursive schemes for n ≥ 3 that improve upon all previous fully explicit schemes for a wide range of parameters.
This work was supported in part by NSERC, the Canada Research Chairs program, a David Cheriton Scholarship, and a Derick Wood Graduate Scholarship.
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Lewenstein, M., Munro, J.I., Nicholson, P.K., Raman, V. (2014). Improved Explicit Data Structures in the Bitprobe Model. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_52
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DOI: https://doi.org/10.1007/978-3-662-44777-2_52
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