Communication Complexity

When I was asked to write a contribution for this book about something related to my research, I immediately thought of Communication Complexity. This relatively simple but extremely beautiful and important sub-area of Complexity Theory studies the amount of communication needed for several distributed parties to learn something new. We will review the basic communication model and some of the classical results known for it, sometimes even with proofs. Then we will consider a variant in which the players are allowed to flip fair unbiased coins. We will finish with a brief review of more sophisticated models in which our current state of knowledge is less than satisfactory. All our definitions, statements and proofs are completely elementary, and yet we will state several open problems that have evaded strong researchers for decades.

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