Euclidean SVP is deterministically NP-hard to approximate within any constant factor

Daqing Wan

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arXiv · 2608.12664

Euclidean SVP is deterministically NP-hard to approximate within any constant factor

Daqing Wan

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Abstract

We prove that, for every constant $\rho>1$, the Euclidean shortest vector problem is NP-hard to approximate within any constant factor $\rho$ under a deterministic polynomial-time many-one reduction. This extends our previous deterministic NP-hardness result from $\rho<\sqrt 2$ to arbitrary constants and gives a deterministic version of Khot's randomized arbitrary-constant theorem.

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Daqing Wan. 2026-08-12. Euclidean SVP is deterministically NP-hard to approximate within any constant factor. https://arxiv.org/abs/2608.12664

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