|(complexity)||NP-complete - (NPC, Nondeterministic Polynomial time complete)
A set or property of computational decision problems which
is a subset of NP (i.e. can be solved by a
nondeterministic Turing Machine in polynomial time),
with the additional property that it is also NP-hard. Thus
a solution for one NP-complete problem would solve all
problems in NP. Many (but not all) naturally arising problems
in class NP are in fact NP-complete.|
There is always a polynomial-time algorithm for transforming an instance of any NP-complete problem into an instance of any other NP-complete problem. So if you could solve one you could solve any other by transforming it to the solved one.
The first problem ever shown to be NP-complete was the satisfiability problem. Another example is Hamilton's problem.
See also computational complexity, halting problem, Co-NP, NP-hard.