A discrepancy lower bound for information complexity

Mark Braverman, Omri Weinstein

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

21 Scopus citations

Abstract

This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also applies to information complexity. More precisely, if the discrepancy of a two-party function f with respect to a distribution μ is Disc μ f, then any two party randomized protocol computing f must reveal at least Ω(log(1/Disc μ f)) bits of information to the participants. As a corollary, we obtain that any two-party protocol for computing a random function on {0,1} n × {0,1} n must reveal Ω(n) bits of information to the participants. In addition, we prove that the discrepancy of the Greater-Than function is Ω(1/√n), which provides an alternative proof to the recent proof of Viola [Vio11] of the Ω(log n) lower bound on the communication complexity of this well-studied function and, combined with our main result, proves the tight Ω(log n) lower bound on its information complexity. The proof of our main result develops a new simulation procedure that may be of an independent interest. In a very recent breakthrough work of Kerenidis et al. [KLL +12], this simulation procedure was a building block towards a proof that almost all known lower bound techniques for communication complexity (and not just discrepancy) apply to information complexity.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings
Pages459-470
Number of pages12
DOIs
StatePublished - Aug 28 2012
Event15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012 - Cambridge, MA, United States
Duration: Aug 15 2012Aug 17 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7408 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
CountryUnited States
CityCambridge, MA
Period8/15/128/17/12

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Braverman, M., & Weinstein, O. (2012). A discrepancy lower bound for information complexity. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings (pp. 459-470). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7408 LNCS). https://doi.org/10.1007/978-3-642-32512-0_39