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Clique is hard to approximate within $$n^{1-\epsilon}$$. (English) Zbl 0989.68060
The author of the paper studies the possible performance of a polynomial-time approximation algorithm for the optimization version of the CLIQUE problem, traditionally denoted Max-Clique, which given a graph $$G$$ and an integer $$k$$ tries to identify whether there are $$k$$ nodes all of which are connected in graph $$G$$. The author strengthens the results of Bellare, Goldreich and Sudan who proved that, for any $$\varepsilon> 0$$, Max-Clique cannot be efficiently approximated within $$n^{1/3-\varepsilon}$$, to prove that, for any $$\varepsilon> 0$$, Max-Clique cannot be efficiently approximated within $$n^{1-\varepsilon}$$.

##### MSC:
 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
##### Keywords:
CLIQUE problem; Max-Clique
Full Text:
##### References:
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