Hardness of the Covering Radius Problem on Lattices

I. Haviv, O. Regev
21st Annual IEEE Conference on Computational Complexity (CCC'06)  
We provide the first hardness result for the Covering Radius Problem on lattices (CRP). Namely, we show that for any large enough p ≤ ∞ there exists a constant c p > 1 such that CRP in the ℓ p norm is Π 2 -hard to approximate to within any constant factor less than c p . In particular, for the case p = ∞, we obtain the constant c ∞ = 3/2. This gets close to the factor 2 beyond which the problem is not believed to be Π 2 -hard (Guruswami et al., Computational Complexity, 2005).
doi:10.1109/ccc.2006.23 dblp:conf/coco/HavivR06 fatcat:yhnu35aj7vdx5o5dfsbefsnwg4