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

Yuval Filmus; Hamed Hatami; Yaqiao Li; Suzin You

doi:https://doi.org/10.1007/s00453-018-0484-8

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

Yuval Filmus, Hamed Hatami, Yaqiao Li, Suzin You

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	4200-4237
Number of pages	38
Journal	Algorithmica
Volume	81
Issue number	11-12
DOIs	https://doi.org/10.1007/s00453-018-0484-8
State	Published - 1 Nov 2019

Keywords

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

All Science Journal Classification (ASJC) codes

Computer Science(all)
Computer Science Applications
Applied Mathematics

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title = "Information Complexity of the AND Function in the Two-Party and Multi-party Settings",

abstract = "In a recent breakthrough paper Braverman et al. (in: STOC{\textquoteright}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.",

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AU - Filmus, Yuval

AU - Hatami, Hamed

AU - Li, Yaqiao

AU - You, Suzin

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

KW - AND function

KW - Concavity condition

KW - Information complexity

KW - Multi-party number-in-hand model

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M3 - مقالة

SN - 0178-4617

VL - 81

SP - 4200

EP - 4237

JO - Algorithmica

JF - Algorithmica

IS - 11-12

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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