Densest Subgraph

The densest subgraph problem focuses on identifying a subset of nodes within a graph that maximizes a chosen density measure, often average degree or a generalized p-mean. Current research explores efficient algorithms, including variations of peeling algorithms and approaches leveraging semidefinite relaxations, to solve this computationally challenging problem, particularly for large graphs and weighted graphs representing diverse data relationships. Applications range from novel image discovery and robust data association to enhancing hypergraph neural networks and securing federated learning against malicious actors, highlighting the problem's broad impact across various fields.