Multiparty Communication Complexity of Collision Finding
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910695203799040 |
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| author | Beame, Paul Whitmeyer, Michael |
| author_facet | Beame, Paul Whitmeyer, Michael |
| contents | We prove an $Ω(n^{1-1/k} \log k \ /2^k)$ 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 $2^{Ω(\sqrt{n})}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07400 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiparty Communication Complexity of Collision Finding Beame, Paul Whitmeyer, Michael Computational Complexity We prove an $Ω(n^{1-1/k} \log k \ /2^k)$ 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 $2^{Ω(\sqrt{n})}$. |
| title | Multiparty Communication Complexity of Collision Finding |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2411.07400 |