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New Sampling Lower Bounds via the Separator

Author Emanuele Viola

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LIPIcs.CCC.2023.26.pdf
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Author Details

Emanuele Viola
  • Khoury College of Computer Sciences, Northeastern University, Boston, MA, USA

Funding

  • Viola, Emanuele: Supported by NSF CCF award 2114116.

Acknowledgements

We thank the anonymous reviewers for detailed and helpful feedback.

Cite As Get BibTex

Emanuele Viola. New Sampling Lower Bounds via the Separator. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 26:1-26:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CCC.2023.26

Abstract

Suppose that a target distribution can be approximately sampled by a low-depth decision tree, or more generally by an efficient cell-probe algorithm. It is shown to be possible to restrict the input to the sampler so that its output distribution is still not too far from the target distribution, and at the same time many output coordinates are almost pairwise independent.
This new tool is then used to obtain several new sampling lower bounds and separations, including a separation between AC0 and low-depth decision trees, and a hierarchy theorem for sampling. It is also used to obtain a new proof of the Patrascu-Viola data-structure lower bound for Rank, thereby unifying sampling and data-structure lower bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Circuit complexity
Keywords
  • Sampling
  • data structures
  • lower bounds
  • cell probe
  • decision forest
  • AC0
  • rank
  • predecessor

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