A Communication Lower Bounds Using Directional Derivatives
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چکیده
We study the set disjointness problem in the most powerful model of bounded-error communication, the k-party randomized number-on-the-forehead model. We show that set disjointness requires Ω( √ n/2kk) bits of communication, where n is the size of the universe. Our lower bound generalizes to quantum communication, where it is essentially optimal. Proving this bound was a longstanding open problem even in restricted settings, such as one-way classical protocols with k = 4 parties (Wigderson 1997). The proof contributes a novel technique for lower bounds on multiparty communication, based on directional derivatives of protocols over the reals.
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تاریخ انتشار 2014