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 over the last five decades, with many variants proposed and many applications built on top of this basic definition. Recent years have witnessed a revival of research interest on this problem with several interesting 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 on 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：稠密子图问题需要在给定的图中找到一组顶点，使得诱导子图的密度尽可能大。在过去的五十年里，该问题在算法文献中受到了极大的关注，提出了许多变体并建立了许多应用。近年来，这一问题在研究领域中重新受到关注，2022年和2023年出版了许多重要的成果。本综述全面展示了基础性结果并详细介绍了文献中提出的许多变体，尤其关注最近的结果。综述还全面展示了应用方面的概述，并讨论了一些有趣的开放问题，这是一个持久的研究主题。