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.

翻译：稠密子图问题要求在图论中寻找一个顶点子集，使其诱导子图最大化某种密度度量。自20世纪70年代初以来，该问题在算法文献中备受关注，衍生出众多变体，并基于这一基本定义构建了大量应用。近年来，该问题重新成为研究热点，涌现出多项重要贡献，包括2022年和2023年发表的若干突破性成果。本综述深入梳理了基础性结论，全面覆盖文献中提出的多种变体，并特别关注最新研究进展。同时，本文系统介绍了相关应用，并探讨了该长青研究主题中若干值得关注的开放问题。