minidxksiS

MinidxksiS is a theoretical framework and algorithmic approach used in discrete optimization to identify a minimal subset of indices that satisfies a family of constraints defined over indexed elements. The central task is to find the smallest index set I such that a specified predicate P is satisfied when restricted to the elements whose positions lie in I. The concept is described as a generalization of index-based covering and independence problems, with a focus on minimality of the index set rather than of the data subset.

Formalization typically begins with a finite universe U = {1,...,n}, a collection of constraints C, and a predicate P(I) that depends on the indices in I. The minidxksiS problem asks for I ⊆ U of minimum cardinality satisfying P. The problem is NP-hard in general; exact methods are exponential in n, while special cases with structured constraints allow polynomial-time solutions. Practical work often relies on greedy heuristics, local search, or mixed-integer programming.

Applications span feature selection in machine learning, sensor placement, and data summarization, where one seeks to preserve performance or coverage with as few indices as possible. It has been studied as a way to reduce dimensionality, enforce sparsity in representations, or minimize monitoring costs while maintaining a target level of information.

Related concepts include the minimum set cover, hitting set, and minimum dominating set problems, as well as submodular optimization techniques. Variants of minidxksiS may weight indices, require robustness to perturbations, or optimize multiple criteria such as cost and accuracy.