Before revision: The problem of nearest-neighbor  condensation deals with finding a subset R from a set of labeled points P such that for every point p \in P the nearest-neighbor of p in R has the same label as p.
After revision: Given a training set P of labeled points, the nearest-neighbor condensation deals with finding a subset R from a set of labeled points P such that for every point p \in P the nearest-neighbor of p in R has the same label as p.