Affiliation:
1. University of California, Los Angeles, CA
Abstract
We study the set disjointness problem in the most powerful model of bounded-error communication, the
k
-party randomized number-on-the-forehead model. We show that set disjointness requires Ω(√n/2
k
k
) bits of communication, where
n
is the size of the universe. Our lower bound generalizes to quantum communication, where it is essentially optimal. Proving this bound was a longstanding open problem even in restricted settings, such as one-way classical protocols with
k
=4 parties [Wigderson 1997]. The proof contributes a novel technique for lower bounds on multiparty communication, based on directional derivatives of protocols over the reals.
Funder
Division of Computing and Communication Foundations
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
45 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. The approximate degree of DNF and CNF formulas;Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing;2022-06-09
2. Approximate Degree in Classical and Quantum Computing;Foundations and Trends® in Theoretical Computer Science;2022
3. Lower Bounds on OBDD Proofs with Several Orders;ACM Transactions on Computational Logic;2021-10-31
4. Near-Optimal Lower Bounds on the Threshold Degree and Sign-Rank of AC$^0$;SIAM Journal on Computing;2021-08-20
5. The hardest halfspace;computational complexity;2021-08-03