(definition)

**Definition:**
A theoretical measure of the execution of an *algorithm*, usually the time or memory needed, given the problem size n, which is usually the number of items. Informally, saying some equation f(n) = ω (g(n)) means g(n) becomes insignificant relative to f(n) as n goes to infinity.

**Formal Definition:** f(n) = ω (g(n)) means that for any positive constant c, there exists a constant k, such that 0 ≤ cg(n) < f(n) for all n ≥ k. The value of k must not depend on n, but may depend on c.

**See also**
*Ω(n)*, *little-o notation*, *big-O notation*.

*Note:
This is the Greek letter Omega.*

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified 29 November 2004.

HTML page formatted Fri Mar 25 16:20:33 2011.

Cite this as:

Paul E. Black, "ω", in
*Dictionary of Algorithms and Data
Structures* [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 29 November 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/omega.html