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：密集子图问题是指在给定图中找到一个顶点子集，使得其诱导子图最大化某种密度度量。过去五十年来，该问题在算法文献中受到了广泛关注，衍生出多种变体，并基于该基本定义构建了许多应用。近年来，该问题的研究兴趣重新焕发，涌现出多项重要成果，包括于2022年和2023年发表的一些突破性结果。本综述深入概述了基础研究成果，全面覆盖了文献中提出的众多变体，并特别关注最新进展。同时，综述还系统梳理了相关应用，并讨论了这一经典研究课题中若干有趣的开放问题。