The linear-array conjecture in communication complexity is false

Eyal Kushilevitz, Nathan Linial, Rafail Ostrovsky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

A linear array network consists of k + 1 processors P0, P1,..., Pk with links only between Pi and Pi+i (0 ≤ i < k). It is required to compute some boolean function f(x, y) in this network, where x is initially stored at P0 and y at Pk. Let Dk(f) be the (total) number of bits that must be exchanged to compute/in worst case. Clearly, Dk(f) ≤ k · D(f), where D(f) is the standard two-party communication complexity of/. Tiwari proved that for almost all functions Dk(f) ≥ k(D(f) - 0(1)) and conjectured that this is true for all functions. In this paper we disprove Tiwari's conjecture, by exhibiting an infinite family of functions for which Dk(f) is essentially at most 3/4k · D(f). This construction also leads to progress on another major problem in this area: It is easy to bound the two-party communication complexity of any function, given the least number of monochromatic rectangles in any partition of the input space. How tight are such bounds? We exhibit certain functions, for which the (two-party) communication complexity is twice larger than the best lower bound obtainable this way.

Original languageAmerican English
Title of host publicationProceedings of the 28th Annual ACM Symposium on Theory of Computing, STOC 1996
PublisherAssociation for Computing Machinery
Pages1-10
Number of pages10
ISBN (Electronic)0897917855
DOIs
StatePublished - 1 Jul 1996
Event28th Annual ACM Symposium on Theory of Computing, STOC 1996 - Philadelphia, United States
Duration: 22 May 199624 May 1996

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F129452
ISSN (Print)0737-8017

Conference

Conference28th Annual ACM Symposium on Theory of Computing, STOC 1996
Country/TerritoryUnited States
CityPhiladelphia
Period22/05/9624/05/96

Bibliographical note

Publisher Copyright:
© 1996 ACM.

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