A Novel Approximation Algorithm for the Shortest Vector Problem - Ajitha Shenoy, K. B. (IEEE access, 2024)
Finding the shortest vector in a lattice is a NP-hard problem. The best known approximation algorithm for this problem is LLL algorithm with the approximation factor of α ^{\frac {n-1}{2}} , α ≥ \frac {4}{3} , which is not a good approximation factor. This work proposes a new polynomial time approximation algorithm for the shortest lattice vector problem. The proposed method makes use of only integer arithmetic and does not require Gram-Schmidt orthogonal basis for generating reduced basis. The proposed method is able to obtain an approximation factor of \frac {1}{(1-δ)} , where 0 ≤ δ \lt 1 .