Deterministic polynomial-time approximation scheme for the permanent

Develop a deterministic fully polynomial-time approximation scheme for computing the permanent of arbitrary nonnegative matrices, improving on exponential-in-fn approximation guarantees.

Background

The permanent of a nonnegative matrix is exactly computable only at prohibitive complexity in general, while Jerrum, Sinclair, and Vigoda established a fully polynomial randomized approximation scheme. Before the result presented in the paper, known deterministic polynomial-time algorithms achieved only approximation factors exponential in the matrix dimension. The paper proves a deterministic strongly polynomial algorithm with approximation factor $(1+\varepsilon)^n$, but this remains exponential in $n$ for fixed \varepsilon and therefore does not resolve the broader goal of a deterministic fully polynomial-time approximation scheme.