Before revision:  However, we show that a slight variation of this adaptive k-means algorithm can be efficiently implemented on relational data, and that this alternative algorithmhas the same performance guarantee as the original algorithm , that is that it outputs an O(1)-approximate sketch .
After revision:  However, we show that a slight variation of this adaptive k-means algorithm can be efficiently implemented on relational data, and that this alternative algorithmhas the same performance guarantee as the original algorithm , that is that it outputs an O(1)-approximate k-means solution .