minimumát

Minimumát is a theoretical construct used in optimization and decision theory to denote the smallest subset of elements required to guarantee a specified outcome under a given model. The term is a neologism—formed from the word minimum and a suffix used to derive abstract nouns—and is encountered in discussions of minimal representations, pruning, and efficient design. A subset S of a universal set U is a minimumát for a property P with respect to a model M if (1) P holds when inputs are restricted to S, and (2) no proper subset of S satisfies P under M.

Computation and complexity: Finding a minimumát is generally computationally challenging. In many settings the problem is NP-hard, and exact search scales poorly with the size of U. Practical methods include greedy selection, backward elimination, and local search; when the property P is submodular, approximation guarantees can be derived. In some domains, the minimumát concept aligns with or is contained in the idea of a core-set, a small representative subset that approximates the full dataset.

Applications and examples: In sensor networks, a minimumát would be the smallest set of sensor locations needed to guarantee full area coverage under a prescribed tolerance. In machine learning, a minimumát corresponds to the smallest feature subset that preserves required predictive performance on a validation set. In software testing, it can describe the minimal set of test cases needed to detect a given class of defects.

Limitations and related terms: The size and composition of a minimumát depend on the chosen model M, the property P, and the data. Different models or objectives yield different minimumát sets. Related concepts include core-set, minimal hitting set, and feature selection.