Inapproximability Results for the Closest Vector Problem with Preprocessing over infty Norm.
Wenbin Chen, Jiangtao Meng · Electronic colloquium on computational complexity · 2006
We show that the Closest Vector Problem with Preprocessing over `∞ norm (CVPP∞) is NP-hard to approximate to within a factor of (log n)1/2− , unless NP⊆ DTIME (2polylog(n)). The result is the same as that in [19] by Regev and Rosen, but our proof methods are different from theirs. Their reductions are based on norm embeddings. However, our reductions are based on the reduction of [2] and the property of Hadamard matrix.