An $n$ dimensional lattice is the set of integer linear combinations of $n$ linearly independent vectors in $\mathbb{R}^{d}$ ($d\le n$). The $n$ independent vectors are called the basis of the lattice, and $L$ is the lattice generated by those vectors.
SVP (Shortest Vector Problem) is the following: given a basis $\mathbf{b}_{1},\mathbf{b}_{2},\ldots,\mathbf{b}_{n}\in\mathbb{R}^{d}$ ($n\le d$) of a lattice $L$, find $\mathbf{x}\in L\setminus \{0\}$ such that $\|\mathbf{x}\|_{2}$ is minimal among vectors of $L\setminus \{0\}$.
The length of the shortest non-zero vector of a lattice $L$ is denoted as $\lambda_{1}(L)$. One can also describe the approximation version of the problem:
SVP$_{\gamma}$ given a basis $\mathbf{b}_{1},\mathbf{b}_{2},\ldots,\mathbf{b}_{n}\in\mathbb{R}^{d}$ ($n\le d$) of a lattice $L$, find $\mathbf{x}\in L\setminus \{0\}$ such that $\|\mathbf{x}\|_{2}\le \gamma(n)\cdot\lambda_{1}(L)$ ($\gamma$ is a function of $n$).
My question is the following: Can we somehow use the approximate version of the problem to solve the original one?
SVP is thought to be NP-hard even though it is not proven. Current state of the art algorithms either run in $2^{O(n)}$ time and space or $O(n^{n})$ time and polynomial space (SVP). I was wondering if there is any way to speed things up given a polynomial time subroutine that solves the approximate version of the problem. Also how many calls do we need to the subroutine depending on $\gamma$?