  Prior optimal CUR decomposition and near optimal column reconstruction
methods have been established by combining BSS sampling and adaptive sampling.
In this paper, we propose a new approach to the optimal CUR decomposition and
near optimal column reconstruction by just using leverage score sampling. In
our approach, both the BSS sampling and adaptive sampling are not needed.
Moreover, our approach is the first $O(\mathrm{nnz}(\A))$ optimal CUR algorithm
where $\A$ is a data matrix in question. We also extend our approach to the
Nystr{\"o}m method, obtaining a fast algorithm which runs $\tilde{O}(n^{2})$ or
$O(\mathrm{\nnz}(\A))$
