Affiliation:
1. Stanford, California, CA, USA
2. University of Memphis, Tennessee, USA
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− β
n
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
.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science