The Randomized Communication Complexity of Set Disjointness

We study the communication complexity of the disjointness function, in which each of two players holds a k-subset of a universe of size n and the goal is to determine whether the sets are disjoint. In the model of a common random string we prove that O(k) communication bits are sufficient, regardless of n. In the model of private random coins O(k+ log log n) bits suffice. Both results are asymptotically tight.

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