Efficient maximal cliques enumeration in weakly closed graphs

03/04/2023

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by   George Manoussakis, et al.

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We show that the algorithm presented in [J. Fox, T. Roughgarden, C. Seshadhri, F. Wei, and N. Wein. Finding cliques in social networks: A new distribution-free model. SIAM journal on computing, 49(2):448-464, 2020.] can be modified to have enumeration time complexity α𝒪 (npoly(c)). Here parameter c is the weakly closure of the graph and α its number of maximal cliques. This result improves on their complexity which was not output sensitive and exponential in the closure of the graph.