Multiparty Communication Complexity of Collision Finding

Abstract

We prove an $\hat{I}\text{c◯}(n^{1-1/k}\log k/2^k)$ 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 $2^{\hat{I}\text{c◯}(\sqrt{n})}$.

Withdrawing due to error in proof of main theorem. In particular, it is not clear how to rigorously argue that fake rows/collisions are indistinguishable from the real collisions in our reduction from the disjointness problem