Listimin

Listimin is a theoretical technique used in constraint programming and combinatorial optimization for enumerating minimal candidate subsets that satisfy a given predicate. Given a finite ground set U and a constraint F on subsets of U, Listimin seeks all inclusion-minimal subsets S ⊆ U such that F(S) holds and no proper subset of S also satisfies F.

The term blends list and minimal, reflecting its focus on producing a compact collection of smallest feasible solutions. The concept appears in the literature on solution enumeration, constraint satisfaction, and configuration management, where practitioners need all minimal explanations or configurations that satisfy complex requirements.

Methodologically, Listimin relies on a guided search over the power set of U combined with a feasibility check. A solver tests F on complete or partial subsets. When a subset S satisfies F, it is emitted as a minimal solution only if no known solution is contained in S; the search then prunes any remaining supersets of S to avoid duplicates. If S does not yet satisfy F, elements are added or reconfigured to move toward feasibility, with pruning informed by monotonicity or anti-monotonicity properties of F. Different problem domains implement variations of backtracking, constraint solving, and domain-specific heuristics to improve performance.

Applications of Listimin include product configuration, software feature models, network design, and data-mining tasks that require minimal explanations or configurations. The approach is computationally challenging in general, and practical use depends on the structure of the predicate and the size of the ground set.

See also minimal set, minimal hitting set, constraint satisfaction problem, configuration management.