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Amortized analysis
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==History== Amortized analysis initially emerged from a method called aggregate analysis, which is now subsumed by amortized analysis. The technique was first formally introduced by [[Robert Tarjan]] in his 1985 paper ''Amortized Computational Complexity'',<ref name="tarjan">{{cite journal |last=Tarjan |first=Robert Endre |author-link=Robert Tarjan |title=Amortized Computational Complexity |journal=SIAM Journal on Algebraic and Discrete Methods |date=April 1985 |volume=6 |issue=2 |pages=306β318 |doi=10.1137/0606031 |url=http://www.cs.duke.edu/courses/fall11/cps234/reading/Tarjan85_AmortizedComplexity.pdf |url-status=live |access-date=2024-06-09 |archive-url=https://web.archive.org/web/20150226051958/http://www.cs.duke.edu/courses/fall11/cps234/reading/Tarjan85_AmortizedComplexity.pdf |archive-date=2015-02-26 }}<!--was:http://www.cs.princeton.edu/courses/archive/spr06/cos423/Handouts/Amortized.pdf--></ref> which addressed the need for a more useful form of analysis than the common probabilistic methods used. Amortization was initially used for very specific types of algorithms, particularly those involving [[binary tree]]s and [[Union-find data structure|union]] operations. However, it is now ubiquitous and comes into play when analyzing many other algorithms as well.<ref name="fiebrink"/>
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