Approximate nonnegative rank is equivalent to the smooth rectangle bound

Gillat Kol, Shay Moran, Amir Shpilka, Amir Yehudayoff

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

10 Scopus citations

Abstract

We consider two known lower bounds on randomized communication complexity: The smooth rectangle bound and the logarithm of the approximate nonnegative rank. Our main result is that they are the same up to a multiplicative constant and a small additive term. The logarithm of the nonnegative rank is known to be a nearly tight lower bound on the deterministic communication complexity. Our result indicates that proving the analogue for the randomized case, namely that the log approximate nonnegative rank is a nearly tight bound on randomized communication complexity, would imply the tightness of the information cost bound. Another corollary of our result is the existence of a boolean function with a quasipolynomial gap between its approximate rank and approximate nonnegative rank.

Original languageEnglish (US)
Title of host publicationAutomata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings
PublisherSpringer Verlag
Pages701-712
Number of pages12
EditionPART 1
ISBN (Print)9783662439470
DOIs
StatePublished - Jan 1 2014
Externally publishedYes
Event41st International Colloquium on Automata, Languages, and Programming, ICALP 2014 - Copenhagen, Denmark
Duration: Jul 8 2014Jul 11 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8572 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other41st International Colloquium on Automata, Languages, and Programming, ICALP 2014
CountryDenmark
CityCopenhagen
Period7/8/147/11/14

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kol, G., Moran, S., Shpilka, A., & Yehudayoff, A. (2014). Approximate nonnegative rank is equivalent to the smooth rectangle bound. In Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings (PART 1 ed., pp. 701-712). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8572 LNCS, No. PART 1). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_58