An Approximation Algorithm for the Nearest Decomposable Polynomial in the Hamming Distance

Abstract

A univariate polynomial f is decomposable if it is the composition f = g(h) of polynomials g and h whose degrees are at least two. We consider the nearest decomposable polynomial to a given polynomial f in the Hamming distance. We propose a polynomial-time approximation algorithm for the nearest decomposable polynomial and analyze the quality of the output.