linear

(definition)

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

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified 17 December 2004.
HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:
Paul E. Black, "linear", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/linear.html