Recall the earliest finishing time algorithm from the previous example.

There is a pseudo-polynomial time algorithm using dynamic programming.

Sub-linear time algorithms arise naturally in the investigation of property testing.

For example, an exponential time algorithm can sometimes still be fast enough to make a feasible attack.

Informally, this is true because polynomial time algorithms are closed under composition.

A better exponential time algorithm is known which runs in time O(2).

It is an open problem whether there exists a polynomial time algorithm for calculating rotation distance.

Nevertheless a polynomial time algorithm is not always practical.

That leads to the exponential time algorithm to implement it.

However, non-existence of a polynomial time algorithm does not automatically ensure that the system is secure.