Communication Complexity is NP-hard

Shuichi Hirahara; Rahul Ilango; Bruno Loff

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arXiv · 2507.10426

Communication Complexity is NP-hard

Shuichi Hirahara·Rahul Ilango·Bruno Loff

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Abstract

In the paper where he first defined Communication Complexity, Yao asks: \emph{Is computing $CC(f)$ (the 2-way communication complexity of a given function $f$) NP-complete?} The problem of deciding whether $CC(f) \le k$, when given the communication matrix for $f$ and a number $k$, 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.

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Shuichi Hirahara, Rahul Ilango, Bruno Loff. 2025-07-14. Communication Complexity is NP-hard. https://arxiv.org/abs/2507.10426

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