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Proof verification and hardness of approximation problems
Abstract
The class PCP(f(n),g(n)) consists of all languages L for which there exists a polynomial-time probabilistic oracle machine that used O(f(n)) random bits, queries O(g(n)) bits of its oracle and behaves as follows: If x in L then there exists an oracle y such that the machine accepts for all random choices but if x not in L then for every oracle y the machine rejects with high probability. Arora and Safra (1992) characterized NP as PCP(log n, (loglogn)/sup O(1)/). The authors improve on their result by showing that NP=PCP(logn, 1). The result has the following consequences: (1) MAXSNP-hard problems (e.g. metric TSP, MAX-SAT, MAX-CUT) do not have polynomial time approximation schemes unless P=NP; and (2) for some epsilon >0 the size of the maximal clique in a graph cannot be approximated within a factor of n/sup epsilon / unless P=NP.>
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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
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Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587
Boros, E., & Hammer, P. L. (2002) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(01)00341-9 · Cited by 827
A survey on tree edit distance and related problems
Bille, P. (2005) · Theoretical Computer Science · doi:10.1016/j.tcs.2004.12.030 · Cited by 751
Micali, S. (2000) · SIAM Journal on Computing · doi:10.1137/s0097539795284959 · Cited by 424
Energy Minimization via Graph Cuts: Settling What is Possible
Freedman, D., & Drineas, P. (2005) · 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) · doi:10.1109/cvpr.2005.143 · Cited by 173
Metadata
- Authors
- Arora, S., Lund, C., Motwani, R., Sudan, M., & Szegedy, M.
- Venue
- Proceedings., 33rd Annual Symposium on Foundations of Computer Science
- Publisher
- IEEE
- Published
- 1992
- Pages
- 14-23
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2143391442
- Cited by
- 741
- References
- 2
- FWCI
- 42.81
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Arora, S., Lund, C., Motwani, R., Sudan, M., & Szegedy, M. (1992). Proof verification and hardness of approximation problems. Proceedings., 33rd Annual Symposium on Foundations of Computer Science. https://doi.org/10.1109/sfcs.1992.267823
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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