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In this paper, we propose new deterministic and Monte Carlo interpolationalgorithms for sparse multivariate polynomials represented by straight-lineprograms. Let $f$ be an $n$-variate polynomial given by a straight-lineprogram, which has a degree bound $D$ and a term bound $T$. Our deterministicalgorithm is quadratic in $n,T$ and cubic in $\log D$ in the Soft-Oh sense,which has better complexities than existing deterministic interpolationalgorithms in most cases. Our Monte Carlo interpolation algorithms have bettercomplexities than existing Monte Carlo interpolation algorithms and are thefirst 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 areoptimal in $n$ and $T$ in the Soft-Oh sense.

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