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A Lower Bound for Sampling Disjoint Sets

Published:20 July 2020Publication History
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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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      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
      Issue’s Table of Contents

      Copyright © 2020 ACM

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      Publication History

      • Published: 20 July 2020
      • Accepted: 1 April 2020
      • Revised: 1 March 2020
      • Received: 1 July 2019
      Published in toct Volume 12, Issue 3

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