Applications in Communication Complexity

Abstract

Communication complexity is a basic part of the theory of computational complexity. We have k players who wish to collaboratively evaluate a given function f(x ₁,…,x _n ). The players have unlimited computational power but none of them has access to all inputs x ₁,…,x _n : each player can only see a part of them. The function f itself is known to all players. The players communicate by sending some bits of information about the inputs they can see. The communication complexity of f is then the minimal number of bits communicated on the worst-case input.