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Average Case Complete Problems
Abstract
Many interesting combinatorial problems were found to be NP-complete. Since there is little hope to solve them fast in the worst case, researchers look for algorithms which are fast just “on average”. This matter is sensitive to the choice of a particular NP-complete problem and a probability distribution of its instances. Some of these tasks were easy and some not. But one needs a way to distinguish the “difficult on average” problems. Such negative results could not only save “positive” efforts but may also be used in areas (like cryptography) where hardness of some problems is a frequent assumption. It is shown below that the Tiling problem with uniform distribution of instances has no polynomial “on average” algorithm, unless every NP-problem with every simple probability distribution has it. It is interesting to try to prove similar statements for other NP-problems which resisted so far “average case” attacks.
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Citations
Cited by
Analytic and Algorithmic Solution of Random Satisfiability Problems
Mézard, M., Parisi, G., & Zecchina, R. (2002) · Science · doi:10.1126/science.1073287 · Cited by 1,071
Quantum computational supremacy
Harrow, A. W., & Montanaro, A. (2017) · Nature · doi:10.1038/nature23458 · Cited by 702
Relations between average case complexity and approximation complexity
Feige, U. (2002) · Proceedings of the thiry-fourth annual ACM symposium on Theory of computing · doi:10.1145/509907.509985 · Cited by 351
Modern Cryptography, Probabilistic Proofs and Pseudorandomness
Goldreich, O. (1999) · Algorithms and Combinatorics · doi:10.1007/978-3-662-12521-2 · Cited by 265
One way functions and pseudorandom generators
Levin, L. A. (1987) · Combinatorica · doi:10.1007/bf02579323 · Cited by 257
Self-citation
Metadata
- Authors
- Levin, L. A.
- Venue
- SIAM Journal on Computing
- Published
- 1986-02
- Volume
- 15
- Issue
- 1
- Pages
- 285-286
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2100008268
- Cited by
- 424
- References
- 0
- FWCI
- 3.82
- Type
- journal article
- Language
- en
- Open access
- closed
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- Levin, L. A. (1986). Average Case Complete Problems. SIAM Journal on Computing. https://doi.org/10.1137/0215020
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