Randomized algorithms

Average-case complexity

In computational complexity theory, the average-case complexity of an algorithm is the amount of some computational resource (typically time) used by the algorithm, averaged over all possible inputs. It is frequently contrasted with worst-case complexity which considers the maximal complexity of the algorithm over all possible inputs. There are three primary motivations for studying average-case complexity. First, although some problems may be intractable in the worst-case, the inputs which elicit this behavior may rarely occur in practice, so the average-case complexity may be a more accurate measure of an algorithm's performance. Second, average-case complexity analysis provides tools and techniques to generate hard instances of problems which can be utilized in areas such as cryptography and derandomization. Third, average-case complexity allows discriminating the most efficient algorithm in practice among algorithms of equivalent best case complexity (for instance Quicksort). Average-case analysis requires a notion of an "average" input to an algorithm, which leads to the problem of devising a probability distribution over inputs. Alternatively, a randomized algorithm can be used. The analysis of such algorithms leads to the related notion of an expected complexity. (Wikipedia).

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From playlist Applications of Differentiation – Maximum/Minimum/Optimization Problems

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From playlist Calculus

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From playlist Summer of Math Exposition 2 videos

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Related pages

Symposium on Theory of Computing | Integer factorization | Derandomization | Randomized algorithm | Computational complexity theory | Hamiltonian path problem | Amortized analysis | P (complexity) | Probabilistic analysis of algorithms | Worst-case complexity | Best, worst and average case | Probability distribution | Quicksort | Algorithm | Cryptography | NP (complexity)