Editing Online algorithm (section)

== Definition ==
Because it does not know the whole input, an online algorithm is forced to make decisions that may later turn out not to be optimal, and the study of online algorithms has focused on the quality of decision-making that is possible in this setting. [[Competitive analysis (online algorithm)|Competitive analysis]] formalizes this idea by comparing the relative performance of an online and offline algorithm for the same problem instance. Specifically, the competitive ratio of an algorithm, is defined as the worst-case ratio of its cost divided by the optimal cost, over all possible inputs. The competitive ratio of an online problem is the best competitive ratio achieved by an online algorithm. Intuitively, the competitive ratio of an algorithm gives a measure on the quality of solutions produced by this algorithm, while the competitive ratio of a problem shows the importance of knowing the future for this problem.

=== Other interpretations ===
For other points of view on ''online inputs to algorithms'', see 
* [[streaming algorithm]]: focusing on the amount of memory needed to accurately represent past inputs;
* [[dynamic algorithm]]: focusing on the time complexity of maintaining solutions to problems with online inputs.

=== Examples ===
Some ''online algorithms'':
*[[Insertion sort]]
*[[Perceptron]]
*[[Reservoir sampling]]
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* [[Greedy algorithm]]
* [[Adversary (online algorithm)|Adversary model]]
* [[Metrical task systems]]
* [[Odds algorithm]]
* [[Page replacement algorithm]]
* [[Algorithms for calculating variance]]
* [[Ukkonen's algorithm]]