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Algorithmica

, Volume 81, Issue 11–12, pp 4200–4237 | Cite as

Information Complexity of the AND Function in the Two-Party and Multi-party Settings

  • Yuval Filmus
  • Hamed Hatami
  • Yaqiao LiEmail author
  • Suzin You
Article
  • 56 Downloads
Part of the following topical collections:
  1. Special Issue: Computing and Combinatorics

Abstract

In a recent breakthrough paper Braverman et al. (in: STOC’13, pp 151–160, 2013) developed a local characterization for the zero-error information complexity in the two-party model, and used it to compute the exact internal and external information complexity of the 2-bit AND function. In this article, we extend their results on AND function to the multi-party number-in-hand model by proving that the generalization of their protocol has optimal internal and external information cost for certain natural distributions. Our proof has new components, and in particular, it fixes a minor gap in the proof of Braverman et al.

Keywords

Information complexity AND function Multi-party number-in-hand model Concavity condition 

Notes

Funding

Yuval Filmus is supported by Israel Science Foundation (Grant No. 2022103), Hamed Hatami is supported by an NSERC grant.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Technion — Israel Institute of TechnologyHaifaIsrael
  2. 2.McGill UniversityMontréalCanada

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