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P

The class of algorithms that run in polynomial time is called P.

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Algorithms that require more (exponential) time are ``intractable''
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Some problems seem to inherently require more time
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One class of such problems is Nondeterministically Polynomial (NP), also called polynomial-time verifiable
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Obviously, P $\subseteq$ NP, but P $\subset$ NP (or P = NP) is an open question
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An NP-Complete problem is in NP and is as hard as any problem in NP.
Such a problem not necessarily in NP is called NP-Hard.
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If P = NP, then a large class of NP-Complete problems would have a polynomial-time solution.
Thus, most researchers advocate P $\subset$ NP (P $\neq$ NP)

We would like to know the class to which a problem belongs.


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