Handling unbalanced exponents in multivariate settings

Develop algorithmic techniques that effectively handle unbalanced exponent bit-lengths in multivariate polynomial computation reduced to the univariate case via Kronecker substitution, particularly when exponent sizes vary widely and the usual preservation of total exponent bit-length does not hold.

Background

The authors discuss reducing multivariate polynomials to univariate via Kronecker substitution, a standard approach that can preserve total exponent bit-length when exponent sizes are near the maximum. Their univariate algorithms perform well under this condition.

However, when exponents are highly unbalanced, the preservation fails and efficient handling becomes challenging. The paper explicitly notes that effectively handling unbalanced exponents in these settings remains open.