# Minimal

### From Glossary

In a partially ordered set, a minimal element is one that does not follow another in the ordering. This is not to be confused with minimum.

Another definition pertains to a subset with respect to some
property such that no proper subset has that property. In the 0-1
knapsack problem the set of items not taken is minimal with respect
to the greedy algorithm of adding the most valuable item, if it fits, until
there are no more items than can fit. This does not necessarily
produce a maximum objective value, but the converse is certainly
true: *in order that be an optimal solution,*
*must be minimal with respect to adding
items that fit.* See maximal for
analogy and numerical example.