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[Answers] What is the Meaning of the Notation

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Problem Detail: 

What is meant by saying an algorithm runs in time $Poly(|S|,n,\frac{1}{\epsilon})$.

Can somebody explain with an example.

Asked By : Kumar

Answered By : Shaull

It means that there exists a polynomial $f(x,y,z)$ such that the algorithm runs in time $f(|S|,n,\frac{1}{\epsilon})$.

Specifically, it means that there are constants $c_1,c_2,c_3\ge 0$ such that the algorithm runs in time $O(|S|^{c_1}\cdot n^{c_2}\cdot (\frac{1}{\epsilon})^{c_3})$.

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