A local decision test for sparse polynomials
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Author(s)
Grigorescu, Elena
Jung, Kyomin
Rubinfeld, Ronitt
Date Issued
July 2010
Journal
Information Processing Letters
Publisher
Elsevier
Citation
Grigorescu, Elena; Jung, Kyomin and Rubinfeld, Ronitt. “A Local Decision Test for Sparse Polynomials.” Information Processing Letters 110, no. 20 (September 2010): 898–901.© 2010 Elsevier B.V.
Version
Author's final manuscript
Abstract
An ℓ-sparse (multivariate) polynomial is a polynomial containing at most ℓ-monomials in its explicit description. We assume that a polynomial is implicitly represented as a black-box: on an input query from the domain, the black-box replies with the evaluation of the polynomial at that input. We provide an efficient, randomized algorithm, that can decide whether a polynomial [MathML] given as a black-box is ℓ-sparse or not, provided that q is large compared to the polynomial's total degree. The algorithm makes only queries, which is independent of the domain size. The running time of our algorithm (in the bit-complexity model) is , where d is an upper bound on the degree of each variable. Existing interpolation algorithms for polynomials in the same model run in time . We provide a similar test for polynomials with integer coefficients.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.ipl.2010.07.012
