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arXiv · 1709.08979

Faster Interpolation Algorithms for Sparse Multivariate Polynomials Given by Straight-Line Programs\

Qiao-Long Huang·Xiao-Shan Gao
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Abstract

In this paper, we propose new deterministic and Monte Carlo interpolation algorithms for sparse multivariate polynomials represented by straight-line programs. Let $f$ be an $n$-variate polynomial given by a straight-line program, which has a degree bound $D$ and a term bound $T$. Our deterministic algorithm is quadratic in $n,T$ and cubic in $\log D$ in the Soft-Oh sense, which has better complexities than existing deterministic interpolation algorithms in most cases. Our Monte Carlo interpolation algorithms have better complexities than existing Monte Carlo interpolation algorithms and are the first algorithms whose complexities are linear in $nT$ in the Soft-Oh sense. Since $nT$ is a factor of the size of $f$, our Monte Carlo algorithms are optimal in $n$ and $T$ in the Soft-Oh sense.

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Qiao-Long Huang, Xiao-Shan Gao. 2018-07-17. Faster Interpolation Algorithms for Sparse Multivariate Polynomials Given by Straight-Line Programs\. https://arxiv.org/abs/1709.08979

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