Simplified Lower Bounds on the Multiparty Communication Complexity of Disjointness

We show that the deterministic number-on-forehead communication complexity of set disjointness for k parties on a universe of size n is Ω(n/ 4k). This gives the first lower bound that is linear in n, nearly matching Grolmusz's upper bound of O(log2(n) + k2n/2k). We also simplify the proof of Sherstov's [EQUATION] lower bound for the randomized communication complexity of set disjointness.

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