< complexity > (NPC, Nondeterministic Polynomial time complete) A set or property of computational decision problem s 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 .
http://fi-www.arc.nasa.gov/fia/projects/bayes-group/group/NP/ .
[Other examples?]
(1995-04-10)