A polynomial time algorithm for GapCVPP in l1 norm

This paper concerns the hardness of approximating the closest vector in a lattice with preprocessing in l1 norm, and gives a polynomial time algorithm for GapCVPPγ in l1 norm with gap γ = O(n/logn). The gap is smaller than that obtained by simply generalizing the approach given by Aharonov and Regev. The main technical ingredient used in this paper is the discrete Laplace distribution on lattices which may be of independent interest.

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