How to compress interactive communication

Boaz Barak, Mark Braverman, Xi Chen, Anup Rao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

93 Scopus citations

Abstract

We describe new ways to simulate 2-party communication protocols to get protocols with potentially smaller communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the inputs to the participating parties can be simulated by a new protocol involving at most Õ(√CI) bits of communication. If the protocol reveals I bits of information about the inputs to an observer that watches the communication in the protocol, we show how to carry out the simulation with Õ(I) bits of communication. These results lead to a direct sum theorem for randomized communication complexity. Ignoring polylogarithmic factors, we show that for worst case computation, computing n copies of a function requires √n times the communication required for computing one copy of the function. For average case complexity, given any distribution μ on inputs, computing n copies of the function on n inputs sampled independently according to μ requires √n times the communication for computing one copy. If μ is a product distribution, computing n copies on n independent inputs sampled according to μ requires n times the communication required for computing the function. We also study the complexity of computing the sum (or parity) of n evaluations of f, and obtain results analogous to those above.

Original languageEnglish (US)
Title of host publicationSTOC'10 - Proceedings of the 2010 ACM International Symposium on Theory of Computing
Pages67-76
Number of pages10
DOIs
StatePublished - Jul 23 2010
Externally publishedYes
Event42nd ACM Symposium on Theory of Computing, STOC 2010 - Cambridge, MA, United States
Duration: Jun 5 2010Jun 8 2010

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Other

Other42nd ACM Symposium on Theory of Computing, STOC 2010
CountryUnited States
CityCambridge, MA
Period6/5/106/8/10

All Science Journal Classification (ASJC) codes

  • Software

Keywords

  • communication complexity
  • compression
  • direct sum
  • information theory

Fingerprint Dive into the research topics of 'How to compress interactive communication'. Together they form a unique fingerprint.

Cite this