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On the Advantage of Adaptivity for Sampling with Cell Probes

Authors Farzan Byramji , Daniel M. Kane , Jackson Morris , Anthony Ostuni

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LIPIcs.APPROX-RANDOM.2026.66.pdf
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ACM Subject Classification
  • Theory of computation → Cell probe models and lower bounds
Keywords
  • sampling lower bound
  • cell probe model
  • adaptive sampling

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Abstract

We construct an explicit distribution 𝐃 over {0,1}^N that exhibits an essentially optimal separation between adaptive and non-adaptive cell-probe sampling. The distribution can be sampled exactly when each output bit is allowed two adaptive probes to an arbitrarily long sequence of independent uniform symbols from [N]. In contrast, any non-adaptive sampler requires Ω̃(N) non-adaptive cell probes to generate a distribution with total variation distance less than 1-o(1) from 𝐃. This provides a 2-vs-Ω̃(N) separation for sampling with adaptive versus non-adaptive cell probes, improving upon the 2-vs-Ω̃(log N) separation of Yu and Zhan (ITCS '24) and the (log N)^O(1)-vs-N^Ω(1) separation of Alekseev, Göös, Myasnikov, Riazanov, and Sokolov (STOC '26).

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Farzan Byramji, Daniel M. Kane, Jackson Morris, and Anthony Ostuni. On the Advantage of Adaptivity for Sampling with Cell Probes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 66:1-66:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.66

Author Details

Farzan Byramji
  • UC San Diego, La Jolla, CA, USA
Daniel M. Kane
  • UC San Diego, La Jolla, CA, USA
Jackson Morris
  • UC San Diego, La Jolla, CA, USA
Anthony Ostuni
  • UC San Diego, La Jolla, CA, USA

Funding

  • Byramji, Farzan: Supported by Simons Investigator Award #929894, and NSF Awards CCF-2425349 and AF: Medium 2212136.
  • Kane, Daniel M.: Supported by NSF Medium Award CCF-2107547.
  • Ostuni, Anthony: Partially supported by Simons Investigator Award #929894 and NSF Award CCF-2425349.

Acknowledgements

We are grateful to anonymous reviewers for helpful feedback on an earlier version of this manuscript.

References

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