A Survey on the Densest Subgraph Problem and Its Variants
Tommaso Lanciano, Atsushi Miyauchi, Adriano Fazzone, Francesco Bonchi

TL;DR
This survey comprehensively reviews the Densest Subgraph Problem, its variants, recent breakthroughs, and applications, highlighting ongoing research challenges and future directions in this well-studied area.
Contribution
It provides an exhaustive overview of fundamental results, recent advances, and open problems related to the Densest Subgraph Problem and its variants.
Findings
Recent breakthroughs in 2022-2023 significantly advanced understanding.
The survey covers a wide range of variants and applications.
Open problems remain in algorithm efficiency and problem generalizations.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Optimization and Search Problems · Complexity and Algorithms in Graphs
