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arXiv · 2609.11049

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

Dingding Dong·Vishesh Jain
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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 $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

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Dingding Dong, Vishesh Jain. 2026-09-10. A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix. https://arxiv.org/abs/2609.11049

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