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Hardness and methods to solve CLIQUE

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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.

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Author information

Correspondence to Daming Zhu.

Additional information

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

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Keywords

  • algorithm
  • NP-hardness
  • approximation ratio
  • dynamic programming
  • complexity