Definition: (1) Any function which is a constant times the argument plus a constant: f(x)=c1x + c0. (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], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: