Approximating CVP to Within Almost-Polynomial Factors is NP-Hard

Approximating the SVP to within a Factor

Approximating the SVP to within a Factor (1+1/dimε) Is NP-Hard under Randomized Reductions

✍ Jin-Yi Cai; Ajay Nerurkar 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 172 KB

Recently Ajtai showed that to approximate the shortest lattice vector in the l 2 -norm within a factor (1+2 &dim k ), for a sufficiently large constant k, is NP-hard under randomized reductions. We improve this result to show that to approximate a shortest lattice vector within a factor (1+dim &= ),