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 factorsand sums of univariate polynomials. Our result makes partial progress towards the resolution of the classical question posed by von zur Gathen and Kaltofen in [von zur Gathen/Kaltofen, J. Comp. Sys. Sci., 1985] 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.