The probabilistic communication complexity of set intersection

In the multi-party set disjointness problem, k players receive private inputs in the form of sets X¹, ..., X^k ⊆ [n], and their goal is to check whether their sets intersect. The set intersection problem is similar, except that the players are required to ...

The authors study the direct sum problem with respect to communication complexity: Consider a function f: D to (0, 1), where D contained in (0, 1)/sup n/*(0, 1)/sup n/. The amortized communication complexity of f, i.e. the communication complexity of ...

The main mathematical result of this paper may be stated as follows: Given a matrix M ∈ {-1,1}^{n × n} and any matrix M ∈ R^{n × n} such that sign(M_ij)=M_ij for all i,j, then rank(M)≥n/||M||. Here ||M|| denotes the spectral norm of the matrix M.This implies a ...