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.
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Supported by the National Natural Science Foundation of China (Nos.69873027, 60073042).
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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
- approximation ratio
- dynamic programming