Parameterized complexity of multi-node hubs.

Hubs are high-degree nodes within a network, ubiquitous in complex networks such as telecommunication, biological, social and semantic networks. Here, we do not seek a hub that is a single node, but a hub consisting of k nodes. Formally, given a graph G = (V , E) , we a seek a set A ⊆ V of size k that induces a connected subgraph from which at least p edges emanate. Thus, we identify k nodes which can act as a unit (due to the connectivity constraint) that is a hub (due to the cut constraint). This problem, which we call Multi-Node Hub (MNH), is a variant of the classic Max Cut problem. While it is easy to see that MNH is W[1]-hard with respect to the parameter k , our main contribution is a parameterized algorithm that shows that MNH is FPT with respect to the parameter p. [ABSTRACT FROM AUTHOR]