k-ANN query

$kANN(q)={|R| = k \land \forall x \in R, y \in X - R: d(q, x) \leq (1+\epsilon) d(q, y)}$
where $\epsilon$ represents the approximation error ($\epsilon \geq 0$) and $k$ specifies the size of the returned set.
When $\epsilon=0$ and the 1 , an NN search is performed.