Multiparty Communication Complexity of Collision Finding

Paul Beame; Michael Whitmeyer

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arXiv · 2411.07400

Multiparty Communication Complexity of Collision Finding

Paul Beame·Michael Whitmeyer

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Abstract

We prove an $\Omega(n^{1-1/k} \log k \ /2^k)$ lower bound on the $k$-party number-in-hand communication complexity of collision-finding. This implies a $2^{n^{1-o(1)}}$ lower bound on the size of tree-like cutting-planes proofs of the bit pigeonhole principle, a compact and natural propositional encoding of the pigeonhole principle, improving on the best previous lower bound of $2^{\Omega(\sqrt{n})}$.

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Paul Beame, Michael Whitmeyer. 2024-11-11. Multiparty Communication Complexity of Collision Finding. https://arxiv.org/abs/2411.07400

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