Parallel sparse interpolation using small primes

TL;DR

This paper introduces a heuristic parallel algorithm for sparse polynomial interpolation using small primes, leveraging parallel computing to potentially improve efficiency over traditional methods.

Contribution

It presents a new heuristic parallel interpolation algorithm based on small primes, with an implementation demonstrating practical parallelization benefits.

Findings

Implemented in C with FLINT and MPI

Shows potential for parallel efficiency improvements

Offers an alternative to large prime techniques

Abstract

To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based "big prime" technique, which acts over a single large finite field, or the more recently-proposed "small primes" technique, which reduces the unknown sparse polynomial to many low-degree dense polynomials. While the latter technique has not yet reached the same theoretical efficiency as Prony-based methods, it has an obvious potential for parallelization. We present a heuristic "small primes" interpolation algorithm and report on a low-level C implementation using FLINT and MPI.