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/.

This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
References in periodicals archive ?
The (decision variant of the) MAX CUT is one of the Karp s original NP-complete problems [2] and has long been known to be NP-complete even if the problem is unweighted, that is, if [w.sub.ij] = 1 for all (i,j) [member of] E [3].
Until now, many kinds of P systems can solve some NP-complete problems, such as SAT [4-10], 3coloring problem [11], and Hamiltonian cycle problem [12].
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In this paper, we applied sticker model for solving the knapsack problem which is one of the NP-complete problems.
DNA computing was introduced by Adleman in 1994 who has explained how to use biological tools to solve NP-Complete problems [1, 8].
The class of NP-Complete problems is a subset of NP problems.
[I.sub.1] includes those problems, for which the existing algorithm is a polynomial one, and [I.sub.2] (which includes NP-complete problems), those for which no polynomial time algorithms are known (Koblitz, 1998).
The answer is that it is generally suspected by complexity theorists to be impossible for a quantum computer to solve the SUBSET-SUM problem (and all other problems which share a characteristic with the SUBSET-SUM problem in that they belong to a subclass of NP problems known as NP-complete problems [5]) in polynomial-time.
BAKER, Approximation algorithms for np-complete problems on planar graphs, in Proc.