Finding Disjoint Dense Clubs in an Undirected Graph

In a social network, the trust among its members usually cannot be carried over many hops. So it is important to find disjoint clusters with a small diameter and with a decent size, formally called dense clubs in this paper. This paper focuses on handling this NP-complete problem. First, from the parameterized computational complexity point of view, we show that this problem does not admit a polynomial kernel (implying that it is unlikely to apply some reduction rules to obtain a practically small problem size). Then, we focus on the dual version of the problem, i.e., deleting d vertices to obtain some disjoint dense clubs. We show that this dual problem admits a simple FPT algorithm using a bounded search tree method (the running time is still too high for practical datasets). Finally, we combine a simple reduction rule together with some heuristic method to obtain a practical solution (verified by extensive testing on practical datasets).