Communication Complexity is NP-hard
Computational Complexity
2025-07-15 v1
Abstract
In the paper where he first defined Communication Complexity, Yao asks: \emph{Is computing (the 2-way communication complexity of a given function ) NP-complete?} The problem of deciding whether , when given the communication matrix for and a number , is easily seen to be in NP. Kushilevitz and Weinreb have shown that this problem is cryptographically hard. Here we show it is NP-hard.
Keywords
Cite
@article{arxiv.2507.10426,
title = {Communication Complexity is NP-hard},
author = {Shuichi Hirahara and Rahul Ilango and Bruno Loff},
journal= {arXiv preprint arXiv:2507.10426},
year = {2025}
}