(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

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Entry modified 29 November 2004.

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Cite this as:

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