Abstract
The paper briefly reviews NP-hard optimization problems and their inapproximability. The hardness of solving CLIQUE problem is specifically discussed. A dynamic-programming algorithm and its improved version for CLIQUE are reviewed and some additional analysis is presented. The analysis implies that the improved algorithm, HEWN (hierarchical edge-weighted network), only provides a heuristic or useful method, but cannot be called a polynomial algorithm.
Similar content being viewed by others
References
Cook S. The complexity of theorem-proving procedures. InProceedings of 3rd ACM Symp. Theory of Computing, 1971, pp.151–158.
Karp R M. Reducibility Among Combinatorial Problems. Complexity of Computer Computations, Miller, Thatcher (eds.), Plenum Press, 1972, pp.85–103.
Levin L. Universal search problems.Problemy Peredachi Informatsii, 1973, 9(3): 265–266. (in Russian)
Arora S, Safra S. Probabilistic checking of proofs: A new characterization of NP. InProceedings of 33rd IEEE Symp. Foundations of Computer Science, 1992, pp.2–13.
Arora S, Lund C, Motwani R,et al. Proof verification and intractability of approximation problems. InProceedings of 33rd IEEE Symp. Foundations of Computer Science, 1992, pp.13–22.
Tang Pushan. An algorithm with polynomial time complexity for finding clique in a graph. InProceedings of 5th International Conference on CAD&CG, Shenzhen, P. R. China, 1997, pp.500–505.
Tang Pushan, Huang Zhijun, HEWN: A polynomial algorithm for CLIQUE problem.Journal of Computer Science& Technology, 1998, 13(Supplement): 33–44.
Papadimitriou C, Yannakakis M. Optimization, approximation and complexity classes.J. Computer and System Science, 1991, 43: 425–440.
Berman P, Schnitger G. On the complexity of approximating the independent set problem.Information and Computation, 1992, 96(1): 77–94.
Garey M R, Johnson D S. Computers and Intractability: A Guide to the Theory of NP-Completeness. San Franciso: W. H. Freeman Company, 1979.
Dorit S Hochbaum. Approximation Algorithms for NP-Hard Problems. PWS Publishing Company, 1997.
Feige U, Goldwasser S, Lovasz L,et al. Approximating clique is almost NP-complete. InProceedings of 32nd IEEE Symposium on Foundations of Computer Science, 1991, pp.2–12.
Lund C, Yannakakis M. On the hardness of approximating minimization problems.Journal of the ACM, 1994, 41(5): 960–981.
Zukerman D. NP-complete problems have a version that’s hard to approximate. InProceedings of 8th Structure in Complexity Theory Conference, 1993, pp.305–312.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (Nos.69873027, 60073042).
Rights and permissions
About this article
Cite this article
Zhu, D., Luan, J. & Ma, S. Hardness and methods to solve CLIQUE. J. Comput. Sci. & Technol. 16, 388–391 (2001). https://doi.org/10.1007/BF02948987
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02948987