(definition)

**Definition:**
(1) Proportional to. (2) Asymptotically equal to. 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) ~ g(n) means it grows at the same rate as g(n). More formally, it means lim_{x → ∞}f(x)/g(x) = 1.

**See also**
*big-O notation*, *Θ(n)*, *asymptotically tight bound*.

Author: PEB

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Entry modified 17 December 2004.

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Cite this as:

Paul E. Black, "~", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
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