NP-complete

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NP-complete

(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 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/.

References in periodicals archive ?
Ritchie asked the faculty to contribute ideas for diagrams, reproducing a currently unsolved mathematical problem in computer science called the 'P versus NP problem.
Yet at the present time, if one asks the average mathematician or computer scientist the status of the famous P versus NP problem, he or she will say that it is still open.
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To represent the book I've decided to discuss the chapter on the one problem an amateur might have a chance of solving: The P vs NP Problem.
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We would not say that an algorithm solves the P = NP problem if it assumes a primitive operation that computes an NP-complete function in polynomial time.
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Most people with these NP problems have impairment that does not appear to affect their daily lives; but standard tests can still detect that impairment.
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