Derandomization of Cell Sampling

08/12/2021

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by   Alexander Golovnev, et al.

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Since 1989, the best known lower bound on static data structures was Siegel's classical cell sampling lower bound. Siegel showed an explicit problem with n inputs and m possible queries such that every data structure that answers queries by probing t memory cells requires space s≥Ω(n·(m/n)^1/t). In this work, we improve this bound to s≥Ω(n·(m/n)^1/(t-1)) for all t ≥ 2. For the case of t = 2, we show a tight lower bound, resolving an open question repeatedly posed in the literature. Specifically, we give an explicit problem such that any data structure that probes t=2 memory cells requires space s>m-o(m).