Faster Sparse Interpolation of Straight-Line Programs

@inproceedings{Arnold2013FasterSI,
  title={Faster Sparse Interpolation of Straight-Line Programs},
  author={Andrew Arnold and Mark Giesbrecht and Daniel S. Roche},
  booktitle={CASC},
  year={2013}
}
We give a new probabilistic algorithm for interpolating a "sparse" polynomial f given by a straight-line program. Our algorithm constructs an approximation f * of f, such that f '—' f * probably has at most half the number of terms of f, then recurses on the difference f '—' f *. Our approach builds on previous work by Garg and Schost (2009), and Giesbrecht and Roche (2011), and is asymptotically more efficient in terms of the total cost of the probes required than previous methods, in many… 
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22 Citations
Highly Influential Citations
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Background Citations
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Methods Citations
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Results Citations
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22 Citations

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Faster Deterministic Sparse Interpolation Algorithms for Straight-Line Program Multivariate Polynomials
TLDR
Two new deterministic interpolation algorithms for straightline program multivariate polynomials are proposed with better complexities than existing determinist interpolationgorithms and have similar complexities with existing probabilistic algorithms.
Faster interpolation algorithms for sparse multivariate polynomials given by straight-line programs
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TLDR
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TLDR
A deterministic algorithm to interpolate an m-sparse n-variate polynomial which uses poly(n, m, log H, log d) bit operations and obtains an algorithm for interpolating polynomials represented by arithmetic circuits.
Parallel sparse interpolation using small primes
TLDR
A heuristic "small primes" interpolation algorithm is presented and a low-level C implementation using FLINT and MPI is reported on.
Sparse Polynomial Interpolation Based on Derivative
TLDR
Two new interpolation algorithms for sparse multivariate polynomials represented by a straight-line program(SLP) have been proposed and one has better complexity than existing deterministic algorithms over a field with large characteristic.
Sparse Interpolation of Black-box Multivariate Polynomials using Kronecker Type Substitutions
TLDR
This paper shows that at least half of the terms of f can be recovered from the univariate polynomials obtained from f by three types of Kronecker substitutions, and gives a criterion to check whether these terms really belong to f.
Sparse Polynomial Interpolation over Fields with Large or Zero Characteristic
TLDR
A new interpolation algorithm for a sparse multivariate polynomial represented by a straight-line program (SLP) that is a Monte Carlo randomized algorithm and works over fields with large or zero characteristic.
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