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Local Samplers for Product Distributions

Authors Jordan Horacsek, Chin Ho Lee , Igor Shinkar , Emanuele Viola , Renfei Zhou

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LIPIcs.ICALP.2026.109.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Sampling
  • Succinct data structures
  • Pseudorandomness

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Abstract

We obtain several results on sampling product distributions in a local and randomness-efficient fashion:  
1) Let D = (D_1,D_2,…,D_n) be a product distribution where the D_i have constant support and have dyadic probability masses (i.e., of the form a/2^b where a,b are integers). Then D can be sampled in constant time in the bit-probe model (equivalently, in NC⁰) and randomness complexity (h(D)+ε)n, up to an exponentially small statistical error. The dyadic requirement is necessary.
2) Every p-biased distribution can be sampled in constant time in the cell-probe model with randomness complexity h(p)n + √n ⋅ polylog(n), up to a polynomially small statistical distance.
3) We determine the tradeoffs between locality and statistical distance for sampling the 1/4-biased distribution using non-trivial randomness complexity (e.g., 1.99n). For 2 bit probes, essentially no non-trivial approximation is possible; for 3 bit probes, we give a sampler with 1/poly(n) statistical distance and show that this is best possible; finally, 4 bit probes suffice for exponentially small distance. 
Our constructions rely on pseudorandom distributions that are bounded uniform on average. These distributions are obtained using various tools from low-density parity-check codes, and recent results on succinct and retrieval data structures by Hu, Liang, Yu, Zhang, and Zhou (STOC 2025).

Cite As Get BibTex

Jordan Horacsek, Chin Ho Lee, Igor Shinkar, Emanuele Viola, and Renfei Zhou. Local Samplers for Product Distributions. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 109:1-109:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.109

Author Details

Jordan Horacsek
  • Simon Fraser University, Burnaby, Canada
Chin Ho Lee
  • North Carolina State University, Raleigh, NC, USA
Igor Shinkar
  • Simon Fraser University, Burnaby, Canada
Emanuele Viola
  • Northeastern University, Boston, MA, USA
Renfei Zhou
  • Carnegie Mellon University, Pittsburgh, PA, USA

Funding

  • Viola, Emanuele: Supported by NSF grant CCF-2430026.
  • Zhou, Renfei: Supported in part by Jane Street Graduate Research Fellowship and MongoDB PhD Fellowship.

Acknowledgements

We thank the conference reviewers for their comments. Chin Ho Lee is grateful to Cheuk Ting Li for helpful discussion, in particular for pointing out [Knuth and Yao, 1976] and the references on source simulation.

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