Before revision:  We characterize sufficient conditions to guarantee correct classification of unlabeled points using approximate nearest-neighbor queries on these subsets, which introduces the notion of coresets for classification with the nearest-neighbor rule. Moreover , we prove that it is NP-hard to compute subsets with these characteristics, whose cardinality approximates that of the minimum cardinality subset.
After revision:  We characterize sufficient conditions to correctly classify any query point when using these subsets. Additionally , we prove that it is NP-hard to compute subsets with these characteristics, whose cardinality approximates that of the minimum cardinality subset.