Definition:Big-Omega Notation

Definition
Big-Omega notation is a type of order notation for typically comparing 'run-times' or growth rates between two growth functions.

Suppose $f, g$ are two functions.

Then $f(n) \in \Omega (g(n))$ iff $\exists c > 0, k \ge 0: \forall n > k: f(n) \ge c g(n)$.

This is read as "$f(n)$ is big omega of $g(n)$".

Another method of determining the condition is the following limit:


 * $\displaystyle \lim_{ n \to \infty} {\frac{f(n)}{g(n)}} = c > 0$, where $0 < c \le \infty$.

If such a c does exist, then $f(n) \in \Omega (g(n))$.

To say that $f(n) \in \Omega (g(n))$ is equivalent to $g(n) \in O (f(n))$ where $O$ is the Big O-notation.