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 Omega(n/4^k). This gives the first lower bound that is linear in n, nearly matching Grolmusz\u27s upper bound of O(log^2(n) + k^2n/2^k). We also simplify the proof of Sherstov\u27s Omega(sqrt(n)/(k2^k)) lower bound for the randomized communication complexity of set disjointness

Simulation Theorems via Pseudorandom Properties

We generalize the deterministic simulation theorem of Raz and McKenzie [RM99], to any gadget which satisfies certain hitting property. We prove that inner-product and gap-Hamming satisfy this property, and as a corollary we obtain deterministic simulation theorem for these gadgets, where the gadget's input-size is logarithmic in the input-size of the outer function. This answers an open question posed by G\"{o}\"{o}s, Pitassi and Watson [GPW15]. Our result also implies the previous results for the Indexing gadget, with better parameters than was previously known. A preliminary version of the results obtained in this work appeared in [CKL+17]

Simplified lower bounds on the multiparty communication complexity of disjointness

Non UBCUnreviewedAuthor affiliation: Technion-IITFacult