I. M. Hair

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20242026

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cs.CC2026

Polynomial-Factor Deterministic NP-Hardness for SVP in Every lp Norm with p > 2

Isaac M Hair, Amit Sahai

For every constant $2 < p < \infty$ and every constant \[ 0<\varepsilon< \min\left\{\frac{p-2}{4p},\frac18\right\}, \] we show that the $ℓ_{p}$ -shortest vector problem for lattices of…

cs.CC2026

Deterministic Hardness of Approximation For SVP in all Finite $ℓ_{p}$ Norms

Isaac M Hair, Amit Sahai

We show that, assuming NP $\neq \subseteq$ $\cap_{δ > 0}$ DTIME $(exp n^{δ})$ , the shortest vector problem for lattices of rank $n$ in any finite $ℓ_{p}$ norm is hard to ap…

cs.CC2025

SVP $_{p}$ is Deterministically NP-Hard for all $p > 2$ , Even to Approximate Within a Factor of $2^{l o g^{1 - ε} n}$

Isaac M. Hair, Amit Sahai

We prove that SVP $_{p}$ is NP-hard to approximate within a factor of $2^{l o g^{1 - ε} n}$ , for all constants $ε > 0$ and $p > 2$ , under standard deterministic Kar…

Polynomial-Factor Deterministic NP-Hardness for SVP in Every lp Norm with p > 2

Deterministic Hardness of Approximation For SVP in all Finite ℓp​ Norms

SVPp​ is Deterministically NP-Hard for all p>2, Even to Approximate Within a Factor of 2log1−εn

Deterministic Hardness of Approximation For SVP in all Finite $ℓ_{p}$ Norms

SVP $_{p}$ is Deterministically NP-Hard for all $p > 2$ , Even to Approximate Within a Factor of $2^{l o g^{1 - ε} n}$