(definition)

**Definition:**
(1) Any function which is a constant times the argument plus a constant: f(x)=c_{1}x + c_{0}. (2) In complexity theory, the measure of computation, m(n) (usually execution time or memory space), is bounded by a linear function of the problem size, n. More formally m(n) = *O(n)*.

**See also**
*exponential*, *logarithmic*, *polynomial*.

*Note:
Strictly speaking, a linear function is polynomial with the highest exponent being 1. However polynomial usually means exponents greater than 1.*

Author: PEB

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Entry modified 17 December 2004.

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Cite this as:

Paul E. Black, "linear", 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/linear.html