Abstract
We show SVP∞ and CVP∞ to be NP-hard to approximate to within n c/loglogn for some constant c > 0. We show a direct reduction from SAT to these problems, that combines ideas from [ABSS93] and from [DKRS99], along with some modifications. Our result is obtained without relying on the PCP characterization of NP, although some of our techniques are derived from the proof of the PCP characterization itself [DFK+99].
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Dinur, I. (2000). Approximating SVP ∞ to within Almost-Polynomial Factors Is NP-Hard. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds) Algorithms and Complexity. CIAC 2000. Lecture Notes in Computer Science, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46521-9_22
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DOI: https://doi.org/10.1007/3-540-46521-9_22
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