# Implicit enumeration

### From Glossary

Applied to integer programming, this is a systematic evaluation of all possible
solutions without explicitly evaluating all of them. For example,
suppose a feasible solution is at hand with objective value 100.
Now suppose we solve a relaxation, such as fixing
some of the variables and solving the resulting linear program, and
we obtain a value of only 90. If we seek a maximum, we can ignore
all possible solutions having the fixed values in the relaxation
since they must all have an objective value of at most 90. This is
often said to be equivalent to branch and bound;
however, the early versions of these methods were related, but
different. The early branch and bound was a *best-first* (even
*breadth-first*) heuristic search
strategy. Early implicit enumeration schemes were
*depth-first*.