Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, July 17, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Anton Krohmer (MPI Saarbrücken)

Finding Cliques in Scale-Free Networks

Finding cliques in graphs is a classical problem which is in general NP-hard and parameterized intractable. However, in typical applications like social networks or protein-protein interaction networks, the considered graphs are scale-free, i.e., their degree sequence follows a power law. Their specific structure can be algorithmically exploited and makes it possible to solve clique much more efficiently. We prove that on inhomogeneous random graphs with n nodes and power law exponent ɣ, cliques of size k can be found in time O(n^2) for ɣ ≥ 3 and in time O(n*exp(k^4)) for 2 < ɣ < 3.

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