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How to Compress Asymmetric Communication

Authors Sivaramakrishnan Natarajan Ramamoorthy, Anup Rao

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Sivaramakrishnan Natarajan Ramamoorthy
Anup Rao

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Sivaramakrishnan Natarajan Ramamoorthy and Anup Rao. How to Compress Asymmetric Communication. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 102-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CCC.2015.102

Abstract

We study the relationship between communication and information in 2-party communication protocols when the information is asymmetric. If I^A denotes the number of bits of information revealed by the first party, I^B denotes the information revealed by the second party, and C is the number of bits of communication in the protocol, we show that i) one can simulate the protocol using order I^A + (C^3 *  I^B)^(1/4) * log(C) + (C * I^B)^(1/2) * log(C)  bits of communication, ii) one can simulate the protocol using order I^A * 2^(O(I^B)) bits of communication  The first result gives the best known bound on the complexity of a simulation when I^A >> I^B,C^(3/4). The second gives the best known bound when I^B << 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.

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Keywords
  • Communication Complexity
  • Interactive Compression
  • Information Complexity

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