There are growing interests in designing polynomial-time approximation schemes (PTAS) for optimization problems in planar graphs. Many NP-hard problems are shown to admit PTAS in planar graphs in the last decade, including Steiner tree, Steiner forest, two- edge-connected subgraphs and so on. We follow this research line and study several...
In real networks, identifying dense regions is of great importance. For example, in a network that represents academic collaboration, authors within the densest component of the graph tend to be the most prolific. Dense subgraphs often identify communities in social networks. And dense subgraphs can be used to discover regulatory...