NP-complete definition complexity
(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
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