How to Compress Asymmetric Communication

We study the relationship between communication and information in 2-party communication protocols when the information is asymmetric. If I denotes the number of bits of information revealed by the first party, I 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 I + 4 √ C3 · IB · logC + √ C · IB · logC bits of communication, one can simulate the protocol using order I · 2O(IB) bits of communication. The first result gives the best known bound on the complexity of a simulation when I I , C3/4. The second gives the best known bound when I logC. 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. 1998 ACM Subject Classification F.1.2 Modes of Computation