What is a "Natural" NP-Complete prob?

Question

I think I have a pretty decent understanding of NP-Complete, NP-Hard, etc. in general, but all of a sudden, stumbling upon some literature, I found someone saying a "natural" NP-complete problem -- explicitly with those quotes. I didn't understand what they meant, so I tried to google it -- it popped up several more times, but no one ever bothered explaining what they meant by "natural".

Can someone explain to me what the context is for putting quotes around "natural" -- what does one mean when they say a "natural" NP-complete problem?

Answer 1

In the context of CS theory, you often see someone prove that there are problems with certain properties by defining highly contrived problems that no one would likely actually encounter in practice. For example, Ladner's theorem shows that if P ≠ NP, then there is a problem in NP that isn't in P but also isn't NP-complete, but the specific problem devised is highly contrived and, essentially, was constructed for the sole purpose of having the indicated property. These problems, subjectively, are referred to as "unnatural" problems because the problem was invented to have some property.

A "natural" problem is a problem that, subjectively, is interesting in its own right - usually, something that's been studied before - that is later shown to have some interesting theoretical property. In that context, a "natural" NP-complete problem would be an NP-complete problem that actually arises in practice - say, something like 3-colorability, the Hamiltonian cycle problem, or boolean satisfiability.