I’d like to say that a certain complexity class is the least-complex for solving an NP-complete problem. How could I say that correctly? For instance, I’d say O(n^2) is more complex than O(n). So O(n) is less complex than O(n^2). Also, there’s no comparison-based sort that’s less complex than O(n log n). So O(n log n) is the least complex complexity-class for sorting. (Am I saying this right? How should I say it?)

Here’s a paragraph I’d like to write. What do you think?

We show the NP-complete problem X can be solved in time O(T) by an exact algorithm. Therefore, X is an NP-complete problem having an exact algorithm in the least-complex complexity class among all NP-complex problems. (That’s what’s interesting about X.)

Any comparison sort algorithm is in the class Omega(n log n).

https://en.wikipedia.org/wiki/Big_O_notation#The_Knuth_definition