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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.

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History and background

Donald KnuthArt of Computer ProgrammingNP-completeLeonid LevinNP
5 related topics

Applications

One-way functionsOpen problemInteger factorizationDiscrete logCoNP
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If and only ifTrade-offComplexity class
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Reductions between distributional problems

Halting ProblemEXPNEXP
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Average-case complexity

Nodes35
Edges34
Triples81
Avg. degree1.94
Density0.057143
Components1

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Average-case complexity

Top relations

related to Further reading · 49
Average-case complexity → Alan, Average, Average Case Complexity, Average-case, Barak, Berlin, Boaz, Business Media, Cambridge, Cambridge University Press, Complexity, Complexity Theory, Computation, Computational Complexity, Computer Science, Cryptography, Goldreich, Heidelberg, IEEE Comput, Impagliazzo
related to history · 11
Average-case complexity → An, Art, Computer Programming, Donald Knuth, However, In, Much, NP-complete, The, Thus, Volume
related to Cryptography · 8
Average-case complexity → Although, For, In, Note, NP, NP-complete, The, Thus
related to Other results · 7
Average-case complexity → Andrew Yao, Applying, Impagliazzo, In, Levin, NP, Yao's
related to Sorting algorithms · 3
Average-case complexity → As, For, Quicksort

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Important terminology

complexity average-case algorithm problems problem average algorithms time inputs worst-case case distribution efficient polynomial np distnp-complete theory possible distributional input

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SubjectPredicateObjectConfidenceSrc
cryptographyinstance ofaverage-case complexity analysis provides tools and techniques to generate hard instances of problems which can be utilized in areas0.80text
derandomizationinstance ofaverage-case complexity analysis provides tools and techniques to generate hard instances of problems which can be utilized in areas0.80text
integer factorization or computing the discrete loginstance ofmany candidate one-way functions are based on hard problems0.80text
Average-case complexityrelated to CryptographyFor0.60section
Average-case complexityrelated to CryptographyIn0.60section
Average-case complexityrelated to CryptographyThus0.60section
Average-case complexityrelated to CryptographyAlthough0.60section
Average-case complexityrelated to CryptographyNote0.60section
Average-case complexityrelated to CryptographyNP-complete0.60section
Average-case complexityrelated to CryptographyNP0.60section
Average-case complexityrelated to CryptographyThe0.60section
Average-case complexityrelated to Further readingPedagogical0.60section

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