# What is the Meaning of the Notation [duplicate]

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

Can somebody explain with an example.

• This is hard to answer without any context. Notation often depends upon the context in which it is used. Will not migrate to Computer Science until the question is improved. Mar 5, 2013 at 9:58
• @DaveClarke: I don't think this is ambiguous; Schaull's answer is exactly right. Mar 5, 2013 at 18:51
• @HuckBennett: Perhaps it is simply a matter of unfamiliarity on my part (and the OP's). Mar 5, 2013 at 19:02

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 $O(|S|^{c_1}\cdot n^{c_2}\cdot (\frac{1}{\epsilon})^{c_3})$.
• Because that's how polynomials work - you're allowed to multiply factors by one another. To make this a little more concrete, think of a polynomial $f(x,y,z)$, then $x\cdot f(x,y,z)$ is also a polynomial, and then you have to multiply the monomials by one another. Dec 13, 2014 at 19:01
• Thanks, so then conceivably you could also have something like: $O((|S| + someconstant)^{c_1} \cdot (n - 2)^{c_2} * (\frac{1}{\epsilon})^{c_3})$ as well? Dec 13, 2014 at 19:10