Although any given solution to an NP-complete problem can be verified quickly (in polynomial time), there is no known efficient way to locate a solution in the first place; indeed, the most notable characteristic of NP-complete problems is that no fast solution to them is known. That is, the time required to solve the problem using any currently k...
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http://en.wikipedia.org/wiki/NP-complete
Problems are divided into two categories: those for which there exists an algorithm to solve it with polynomial time complexity, and those for which there is no such algorithm. We denote the former class of problems by P. There are problems for which no known algorithm exists that solves it in polynomial time, but there is also no proof that no su....
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http://glossary.computing.society.informs.org/index.php?page=N.html
A problem type in which any instance of any other NP class problem can be translated to in polynomial time. This means that if a fast algorithm exists for an NP-complete problem, then any problem that is in NP can be solved with the same algorithm.
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http://www.encyclo.co.uk/local/20090
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