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In this work we propose a method for computing a minimum size training set consistent subset for the Nearest Neighbor rule (also said CNN problem) via SAT encodings. We introduce the SAT–CNN algorithm, which exploits a suitable encoding of the CNN problem in a sequence of SAT problems in order to exactly solve it, provided that enough computational resources are available. Comparison of SAT–CNN with well-known greedy methods shows that SAT–CNN is able to return a better solution. The proposed approach can be extended to several hard subset selection classification problems.

Optimal Subset Selection for Classification through SAT Encodings