The maximum clique problem is a very well-known NP-complete problem of the kind for which meta-heuristic algorithms, which include ant algorithms, have been developed. Well-known instances of problems enable the assessment of the quality of elaborated algorithms; however, there is a particular kind of graph in which each vertex has a nearly equal number of adjacent edges. It is very difficult to find a maximum clique in such a graph. The search for the maximum clique in this particular kind of graph is investigated and compared to the best known ant algorithms.
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