Communication Complexity of Collision

@inproceedings{Gs2022CommunicationCO,
  title={Communication Complexity of Collision},
  author={Mika G{\"o}{\"o}s and Siddhartha Jain},
  booktitle={Electron. Colloquium Comput. Complex.},
  year={2022}
}
The Collision problem is to decide whether a given list of numbers ( x 1 , . . . , x n ) ∈ [ n ] n is 1-to-1 or 2-to-1 when promised one of them is the case. We show an n Ω(1) randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each x i and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov ( CCC… 
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