English

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 CC(f)CC(f) (the 2-way communication complexity of a given function ff) NP-complete?} The problem of deciding whether CC(f)kCC(f) \le k, when given the communication matrix for ff and a number kk, 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}
}
R2 v1 2026-07-01T04:00:15.186Z