Kolmogorov Complexity and Combinatorial Methods in Communication Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Kolmogorov complexity and combinatorial methods in communication complexity
Theoretical Computer Science
Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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In this paper we study the individual communication complexity of the following problem. Alice receives an input string x and Bob an input string y, and Alice has to output y. For deterministic protocols it has been shown in Buhrman et al. (2004), that C(y) many bits need to be exchanged even if the actual amount of information C(y|x) is much smaller than C(y). It turns out that for randomised protocols the situation is very different. We establish randomised protocols whose communication complexity is close to the information theoretical lower bound. We furthermore initiate and obtain results about the randomised round complexity of this problem and show trade-offs between the amount of communication and the number of rounds. In order to do this we establish a general framework for studying these types of questions.