It is a very standard situation that we have a class of problems $P$, and a subclass $\tilde P\subset P$ which has a certain restricted property.
For example, $P$ could be the problem of searching through an arbitrary list of people for someone with height $1.8$ meters, while $\tilde P$ could be the same problem, except that it is known that the list is ordered by height.
Searching through an ordered list is far more efficient than through an arbitrary list.
My question is: what would be the term for an algorithm using/relying on a certain particular structure of the problem in order to run more efficiently than would be needed in the general case?
Or alternatively, what is the term for "omitting calculations" that are necessary to do in the general case but that can be omitted in the restricted problem case?