How to Compress Asymmetric Communication

We study the relationship between communication and information in 2-party communication protocols when the information is asymmetric. If IA denotes the number of bits of information revealed by the first party, IB denotes the information revealed by the second party, and C is the number of bits of communication in the protocol, we show that • one can simulate the protocol using order [EQUATION] bits of communication, • one can simulate the protocol using order IA · 2O(IB) bits of communication. The first result gives the best known bound on the complexity of a simulation when IA G IB,C3/4. The second gives the best known bound when IB L log C. In addition we show that if a function is computed by a protocol with asymmetric information complexity, then the inputs must have a large, nearly monochromatic rectangle of the right dimensions, a fact that is useful for proving lower bounds on lopsided communication problems.