Deterministically Factoring Sparse Polynomials into Multilinear Factors and Sums of Univariate Polynomials

We present the first efficient deterministic algorithm for factoring sparse polynomials that split into multilinear factors and sums of univariate polynomials. Our result makes partial progress towards the resolution of the classical question posed by von zur Gathen and Kaltofen in [6] to devise an efficient deterministic algorithm for factoring (general) sparse polynomials. We achieve our goal by introducing essential factorization schemes which can be thought of as a relaxation of the regular factorization notion. 1998 ACM Subject Classification F.2.1 Numerical Algorithms and Problems Keywords and phrases Derandomization, Multivariate Polynomial Factorization, Sparse polynomials Digital Object Identifier 10.4230/LIPIcs.APPROX-RANDOM.2015.943

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Ilya Volkovich
• Keywords: Algorithms, APPROX 2015