Exponential separation of communication and external information

ANAT GANOR, GILLAT KOL, RAN RAZ

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show an exponential gap between communication complexity and external infor- mation complexity by analyzing a communication task suggested as a candidate by Braverman [A Hard-to-Compress Interactive Task?, in Proceedings of the 51th Annual Allerton Conference on Communication, Control, and Computing, IEEE, 2013]. Previously, only a separation of commu- nication complexity and internal information complexity was known. More precisely, we obtain an explicit example of a search problem with external information complexity at most O(k), with respect to any input distribution, and distributional communication complexity at least 2k, with respect to some input distribution. In particular, this shows that a communication protocol cannot always be compressed to its external information. By a result of Braverman [SIAM J. Comput., 44 (2015), pp. 1698{1739], our gap is the largest possible. Moreover, since the upper bound of O(k) on the ex- ternal information complexity of the problem is obtained with respect to any input distribution, our result implies an exponential gap between communication complexity and information complexity (both internal and external) in the nondistributional setting of Braverman [SIAM J. Comput., 44 (2015), pp. 1698{1739]. In this setting, no gap was previously known, even for internal information complexity.

Original languageEnglish (US)
Pages (from-to)236-254
Number of pages19
JournalSIAM Journal on Computing
Volume50
Issue number3
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics

Keywords

  • Communication complexity
  • Communication compression
  • Information complexity

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