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Recent work proposed -relevant inputs (or sets) as a probabilistic explanation for the predictions made by a classifier on a given input. -relevant sets are significant because they serve to relate (model-agnostic) Anchors with (model-accurate) PI- explanations, among other explanation approaches. Unfortunately, the computation of smallest size -relevant sets is complete for , rendering their computation largely infeasible in practice. This paper investigates solutions for tackling the practical limitations of -relevant sets. First, the paper alternatively considers the computation of subset-minimal sets. Second, the paper studies concrete families of classifiers, including decision trees among others. For these cases, the paper shows that the computation of subset-minimal -relevant sets is in NP, and can be solved with a polynomial number of calls to an NP oracle. The experimental evaluation compares the proposed approach with heuristic explainers for the concrete case of the classifiers studied in the paper, and confirms the advantage of the proposed solution over the state of the art.