A Survey on the Densest Subgraph Problem and Its Variants
It serves as a comprehensive resource for researchers and practitioners interested in graph algorithms, but it is incremental as it synthesizes existing literature without presenting new methods.
This survey provides a deep overview of the Densest Subgraph Problem and its variants, covering fundamental results, recent contributions, applications, and open problems.
The Densest Subgraph Problem requires to find, in a given graph, a subset of vertices whose induced subgraph maximizes a measure of density. The problem has received a great deal of attention in the algorithmic literature since the early 1970s, with many variants proposed and many applications built on top of this basic definition. Recent years have witnessed a revival of research interest in this problem with several important contributions, including some groundbreaking results, published in 2022 and 2023. This survey provides a deep overview of the fundamental results and an exhaustive coverage of the many variants proposed in the literature, with a special attention to the most recent results. The survey also presents a comprehensive overview of applications and discusses some interesting open problems for this evergreen research topic.