Faster sparse interpolation of straight-line programs

TL;DR

This paper introduces a faster probabilistic algorithm for sparse polynomial interpolation from straight-line programs, improving efficiency over previous methods by recursively approximating and reducing the polynomial's complexity.

Contribution

The paper presents a novel probabilistic interpolation algorithm that is asymptotically more efficient than prior approaches, especially in reducing probe costs.

Findings

Algorithm reduces the number of probes needed for interpolation.

Recursion halves the number of polynomial terms at each step.

Method outperforms previous algorithms in many cases.

Abstract

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 their difference probably has at most half the number of terms of f, then recurses on their difference. 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 cases.