Hardness of the Covering Radius Problem on Lattices

Authors:
Ishay Haviv;Oded Regev
Affiliations:
Tel Aviv University, Israel;Tel Aviv University, Israel
Venue:
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Year:
2006

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Abstract

We provide the first hardness result for the Covering Radius Problem on lattices (CRP). Namely, we show that for any large enough p\leqslant\infty there exists a constant cp gt 1 such that CRP in the \ell \rho norm is \Pi®_2-hard to approximate to within any constant less than c_p.