Asymptotic computational complexity
 | This article or section is in a state of significant expansion or restructuring. You are welcome to assist in its construction by editing it as well. If this article or section has not been edited in several days, please remove this template. If you are the editor who added this template and you are actively editing, please be sure to replace this template with {{in use}} during the active editing session. Click on the link for template parameters to use.
This article was last edited by Altenmann (talk | contribs) 17 years ago. (Update timer) |
In computational complexity theory, asymptotic computational complexity is the usage of the asymptotic analysis for the estimation of computational complexity of algorithms and computational problems, commonly associated with the usage of the big O notation.
Since the groundlaying 1965 paper of Hartmanis and Stearns[1] and the 1972 book by Garey and Jackson on NP-completeness, [2] the term "computational complexity" (of algorithms) most commonly refers to the asymptotic computational complexity.
Further, unless specifies otherwise, the term "computational complexity" usually refers to the upper bound for the asymptotic computational complexity of an algorithm or a problem, which is usually written in terms of the "Big Oh", e.g.. Other types of (asymptotic) computational complexity estimates are lower bounds ("Big Omega" notation; e.g., Ω(n)) and asymptotically tight estimates, when the asymptotic upper and lower bounds coincide (written using the "Big Theta"; e.g., Θ(n log n)).
In terms of the most commonly estimated computational resources, it is spoken about the asymptotic time complexity and asymptotic space complexity. Other asymptotically estimated resources include circuit complexity and various measures of parallel computation, such as the number of (parallel) processors.
References
- ^ J. Hartmanis, R. Stearns. "On the computational complexity of algorithms," Transactions of the American Mathematical Society, 1965 vol. 117, pp. 285-306
- ^ Michael Garey, and David S. Johnson: Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W. H. Freeman & Co., 1979.