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 limx → ∞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) Available from: