research-article

A Lower Bound for Sampling Disjoint Sets

Authors:

Thomas WatsonAuthors Info & Claims

ACM Transactions on Computation Theory (TOCT), Volume 12, Issue 3

Article No.: 20, Pages 1 - 13

https://doi.org/10.1145/3404858

Published: 20 July 2020 Publication History

Abstract

Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x⊆ [n] and Bob ends up with a set y⊆ [n], such that (x,y) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant β < 1, this requires Ω (n) communication even to get within statistical distance 1− βⁿ of the target distribution. Previously, Ambainis, Schulman, Ta-Shma, Vazirani, and Wigderson (FOCS 1998) proved that Ω (√n) communication is required to get within some constant statistical distance ɛ > 0 of the uniform distribution over all pairs of disjoint sets of size √n.

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Cited By

Kane DOstuni AWu KMohar BShinkar IO'Donnell R(2024)Locality Bounds for Sampling Hamming SlicesProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649670(1279-1286)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649670
Zhang J(2024)Influence of network video film and television communication based on sampling theoryEntertainment Computing10.1016/j.entcom.2024.10065550(100655)Online publication date: May-2024
https://doi.org/10.1016/j.entcom.2024.100655
Viola E(2023)New Sampling Lower Bounds via the SeparatorProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.26(1-23)Online publication date: 17-Jul-2023
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2023.26

Index Terms

A Lower Bound for Sampling Disjoint Sets
1. Theory of computation
  1. Computational complexity and cryptography
    1. Communication complexity

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cover image ACM Transactions on Computation Theory

ACM Transactions on Computation Theory Volume 12, Issue 3

September 2020

197 pages

ISSN:1942-3454

EISSN:1942-3462

DOI:10.1145/3403647

Editor:
Ryan O'Donnell
Carnegie Mellon University, USA

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Publication History

Published: 20 July 2020

Accepted: 01 April 2020

Revised: 01 March 2020

Received: 01 July 2019

Published in TOCT Volume 12, Issue 3

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Cited By

Kane DOstuni AWu KMohar BShinkar IO'Donnell R(2024)Locality Bounds for Sampling Hamming SlicesProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649670(1279-1286)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649670
Zhang J(2024)Influence of network video film and television communication based on sampling theoryEntertainment Computing10.1016/j.entcom.2024.10065550(100655)Online publication date: May-2024
https://doi.org/10.1016/j.entcom.2024.100655
Viola E(2023)New Sampling Lower Bounds via the SeparatorProceedings of the conference on Proceedings of the 38th Computational Complexity Conference10.4230/LIPIcs.CCC.2023.26(1-23)Online publication date: 17-Jul-2023
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2023.26

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