Before revision:  Then, we generalize our result to give a randomized \alpha-approximation algorithm for any \alpha\in [ 1, \sqrt{n, n / \log n} ], running in time  (n^2/\alpha^2  ).
After revision:  Then, we generalize our result to give a randomized \alpha-approximation algorithm for any \alpha\in [ \sqrt{\log n, n / \log n} ], running in time (n^2/\alpha^2 ).