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Exponential time

From Wikipedia, the free encyclopedia

In complexity theory, exponential time is the computation time of a problem where the time to complete the computation, m(n), is bounded by an exponential function of the problem size, n (i.e, as the size of the problem increases linearly, the time to solve the problem increases exponentially).

Written mathematically, there exists k > 1 such that m(n) = Θ(kn) and there exists c such that m(n) = O(cn).

Computer scientists sometimes think of polynomial time as "fast", and anything slower than that as "slow". Exponential time would therefore be considered slow. There are algorithms which take time slower than polynomial time ("super-polynomial time") but faster than exponential time ("sub-exponential time"). These are also considered "slow". One example is the best known algorithm for integer factorization.

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