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).

Author: PEB

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Entry modified 24 February 2016.
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Paul E. Black, "∼", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 24 February 2016. (accessed TODAY) Available from: