Algorithm for finding smallest collection of components

Question

I\'m looking for an algorithm to solve the following problem. I have a number of subsets (1-n) of a given set (a-h). I want to find the smallest collection of subsets that will

Answer 1

This problem was shown in one the video's of Coursera's Discrete Optimization lectures. IIRC, it's called the set cover problem.

IIRC, it's NP-complete or NP-hard, so look into the typical algorithms (exact algo's for small datasets, metaheuristics for medium/big datasets) and typical frameworks (OptaPlanner, ...)