A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

Abstract: For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $$\operatorname{per} A\le Q\le(1+\varepsilon)^{n\operatorname{per}} A$$.