# potential function

(definition)

**Definition:**
A measure of a data structure whose change after an operation corresponds to the time cost of the operation.

**See also**
*amortized cost*.

*Note:
If an inexpensive operation results in an increase of the potential function, but the increase of the potential function is within a constant factor of the actual cost of the operation, the amortized cost of the operation is unchanged. Meanwhile, if an expensive operation results in a decrease of the potential function that offsets the cost of the expensive operation, the amortized cost of the expensive operation may be small. For such an analysis to remain valid, the potential function must stay nonnegative, and begin with a value of zero. For more on amortized analysis and its origins see Tarjan.*

Author: CLK

## More information

**R. E. Tarjan**, *Amortized computational complexity*, SIAM Journal on Algebraic and Discrete Methods, 6(2):306-318, 1985.

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Entry modified 17 December 2004.

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Cite this as:

Chris L. Kuszmaul, "potential function", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/potentialfnc.html