The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Clique is hard to approximate within n1−ε
Open accessAbstract
We prove that, unless any problem in NP can be solved in proba-bilistic polynomial time, for any > 0, the size of the largest clique in a graph with n nodes is hard to approximate in polynomial time within a factor n 1. This is done by constructing, for any Æ> 0, a proba-bilistically checkable proof for NP which uses logarithmic randomness and Æ amortized free bits. Warning: Essentially this paper has been published in Acta Matehmatica and is subject to copyright restrictions. In particular it is for personal use only. 1
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Citations
Cites
The complexity of theorem-proving procedures
Cook, S. A. (1971) · Proceedings of the third annual ACM symposium on Theory of computing - STOC '71 · doi:10.1145/800157.805047 · Cited by 6,385
Optimization, approximation, and complexity classes
Papadimitriou, C. H., & Yannakakis, M. (1991) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(91)90023-x · Cited by 1,653
Cited by
Some optimal inapproximability results
Håstad, J. (2001) · Journal of the ACM · doi:10.1145/502090.502098 · Cited by 1,902
Self-citationProperty testing and its connection to learning and approximation
Goldreich, O., Goldwasser, S., & Ron, D. (1998) · Journal of the ACM · doi:10.1145/285055.285060 · Cited by 1,020
The overlap gap property: A topological barrier to optimizing over random structures
Gamarnik, D. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2108492118 · Cited by 103
Metadata
- Authors
- Håstad, J.
- Venue
- Acta Mathematica
- Publisher
- International Press of Boston
- Published
- 1999
- Volume
- 182
- Issue
- 1
- Pages
- 105-142
- ISSN
- 0001-5962 (ISSN-L)
- OpenAlex
- W2081254453
- Cited by
- 1,369
- References
- 2
- FWCI
- 66.20
- Type
- journal article
- Language
- en
- Open access
- bronze
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