ϵ-discrepancy sets and their application for interpolation of sparse polynomials

Noga Alon; Yishay Mansour

doi:10.1016/0020-0190(95)00032-8

ϵ-discrepancy sets and their application for interpolation of sparse polynomials

Noga Alon, Yishay Mansour

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

25 Scopus citations

Abstract

We present a simple explicit construction of a probability distribution supported on (p - 1)² vectors in Z_pⁿ, where p ≥ n/ε{lunate} is a prime, for which the absolute value of each nontrivial Fourier coefficients is bounded by ε{lunate}. This construction is used to derandomize the algorithm of Mansour (1992) that interpolates a sparse polynomial in polynomial time in the bit complexity model.

Original language	English
Pages (from-to)	337-342
Number of pages	6
Journal	Information Processing Letters
Volume	54
Issue number	6
DOIs	https://doi.org/10.1016/0020-0190(95)00032-8
State	Published - 23 Jun 1995
Externally published	Yes

Keywords

Analysis of algorithms
Probability analysis
Sparse polynomials

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/0020-0190(95)00032-8

Cite this

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title = "ϵ-discrepancy sets and their application for interpolation of sparse polynomials",

abstract = "We present a simple explicit construction of a probability distribution supported on (p - 1)2 vectors in Zpn, where p ≥ n/ε\{lunate\} is a prime, for which the absolute value of each nontrivial Fourier coefficients is bounded by ε\{lunate\}. This construction is used to derandomize the algorithm of Mansour (1992) that interpolates a sparse polynomial in polynomial time in the bit complexity model.",

keywords = "Analysis of algorithms, Probability analysis, Sparse polynomials",

author = "Noga Alon and Yishay Mansour",

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T1 - ϵ-discrepancy sets and their application for interpolation of sparse polynomials

AU - Alon, Noga

AU - Mansour, Yishay

PY - 1995/6/23

Y1 - 1995/6/23

N2 - We present a simple explicit construction of a probability distribution supported on (p - 1)2 vectors in Zpn, where p ≥ n/ε{lunate} is a prime, for which the absolute value of each nontrivial Fourier coefficients is bounded by ε{lunate}. This construction is used to derandomize the algorithm of Mansour (1992) that interpolates a sparse polynomial in polynomial time in the bit complexity model.

AB - We present a simple explicit construction of a probability distribution supported on (p - 1)2 vectors in Zpn, where p ≥ n/ε{lunate} is a prime, for which the absolute value of each nontrivial Fourier coefficients is bounded by ε{lunate}. This construction is used to derandomize the algorithm of Mansour (1992) that interpolates a sparse polynomial in polynomial time in the bit complexity model.

KW - Analysis of algorithms

KW - Probability analysis

KW - Sparse polynomials

UR - https://www.scopus.com/pages/publications/0029326046

U2 - 10.1016/0020-0190(95)00032-8

DO - 10.1016/0020-0190(95)00032-8

M3 - Article

AN - SCOPUS:0029326046

SN - 0020-0190

VL - 54

SP - 337

EP - 342

JO - Information Processing Letters

JF - Information Processing Letters

IS - 6

ER -

ϵ-discrepancy sets and their application for interpolation of sparse polynomials

Abstract

Keywords

ASJC Scopus subject areas

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