computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand. In

operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...

, the area in which online algorithms are developed is called online optimization. As an example, consider the

sorting algorithms In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is import ...

selection sort and

insertion sort Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. Howev ...

: selection sort repeatedly selects the minimum element from the unsorted remainder and places it at the front, which requires access to the entire input; it is thus an offline algorithm. On the other hand, insertion sort considers one input element per iteration and produces a partial solution without considering future elements. Thus insertion sort is an online algorithm. Note that the final result of an insertion sort is optimum, i.e., a correctly sorted list. For many problems, online algorithms cannot match the performance of offline algorithms. If the ratio between the performance of an online algorithm and an optimal offline algorithm is bounded, the online algorithm is called

competitive Competition is a rivalry where two or more parties strive for a common goal which cannot be shared: where one's gain is the other's loss (an example of which is a zero-sum game). Competition can arise between entities such as organisms, indi ...

. Not every ''offline algorithm'' has an efficient ''online'' counterpart. In grammar theory they are associated with Straight-line grammars.

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 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 In computer science, streaming algorithms are algorithms for processing data streams in which the input is presented as a sequence of items and can be examined in only a few passes, typically one-pass algorithm, just one. These algorithms are desi ...

: 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 Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. Howev ...

Perceptron In machine learning, the perceptron is an algorithm for supervised classification, supervised learning of binary classification, binary classifiers. A binary classifier is a function that can decide whether or not an input, represented by a vect ...

Reservoir sampling Reservoir sampling is a family of randomized algorithms for choosing a simple random sample, without replacement, of items from a population of unknown size in a single pass over the items. The size of the population is not known to the algor ...

Greedy algorithm A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally ...

* Adversary model * Metrical task systems * Odds algorithm * Page replacement algorithm *

Algorithms for calculating variance Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical insta ...

* Ukkonen's algorithm

Online problems

A problem exemplifying the concepts of online algorithms is the Canadian traveller problem. The goal of this problem is to minimize the cost of reaching a target in a weighted graph where some of the edges are unreliable and may have been removed from the graph. However, that an edge has been removed (''failed'') is only revealed to ''the traveller'' when she/he reaches one of the edge's endpoints. The worst case for this problem is simply that all of the unreliable edges fail and the problem reduces to the usual

shortest path problem In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between t ...

. An alternative analysis of the problem can be made with the help of competitive analysis. For this method of analysis, the offline algorithm knows in advance which edges will fail and the goal is to minimize the ratio between the online and offline algorithms' performance. This problem is

PSPACE-complete In computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (PSPACE, polynomial space) and if every other problem that can be solved in polynomial sp ...

. There are many formal problems that offer more than one ''online algorithm'' as solution: * ''k''-server problem * Job shop scheduling problem * List update problem * Bandit problem * Secretary problem * Search games * Ski rental problem * Linear search problem * Portfolio selection problem

References

External links