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In nearest-neighbor classification, a training set $P$ of points in$\mathbb{R}^d$ with given classification is used to classify every point in$\mathbb{R}^d$: Every point gets the same classification as its nearestneighbor in $P$. Recently, Eppstein [SOSA'22] developed an algorithm to detectthe relevant training points, those points $p\in P$, such that $P$ and$P\setminus\{p\}$ induce different classifications. We investigate the problemof finding the minimum cardinality reduced training set $P'\subseteq P$ suchthat $P$ and $P'$ induce the same classification. We show that the set ofrelevant points is such a minimum cardinality reduced training set if $P$ is ingeneral position. Furthermore, we show that finding a minimum cardinalityreduced training set for possibly degenerate $P$ is in P for $d=1$, andNP-complete for $d\geq 2$.

Reducing Nearest Neighbor Training Sets Optimally and Exactly