Hardness and methods to solve CLIQUE
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- 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. CrossRef
- Berman P, Schnitger G. On the complexity of approximating the independent set problem.Information and Computation, 1992, 96(1): 77–94. CrossRef
- 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. CrossRef
- 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.
- Hardness and methods to solve CLIQUE
Journal of Computer Science and Technology
Volume 16, Issue 4 , pp 388-391
- Cover Date
- Print ISSN
- Online ISSN
- Science Press
- Additional Links
- approximation ratio
- dynamic programming
- Industry Sectors