TR13-005 Authors: Alexander A. Sherstov

Publication: 2nd January 2013 22:45

Downloads: 2013

Keywords:

We prove that the set disjointness problem has randomized communication complexity

$\Omega(\sqrt{n}/2^{k}k)$ in the number-on-the-forehead model with $k$ parties, a quadratic improvement

on the previous bound $\Omega(\sqrt{n}/2^{k})^{1/2}$. Our result remains valid for quantum

protocols, where it is essentially tight. Proving it was an open problem since 1997,

even in restricted settings such as one-way classical protocols with $k=4$ parties. We

obtain other near-optimal results for multiparty set disjointness, including an XOR lemma,

a direct product theorem, and lower bounds for nondeterministic and Merlin-Arthur

protocols. The proof contributes a novel technique for lower bounds on multiparty

communication, based on directional derivatives of communication protocols over the reals.