  Dense subgraph extraction is a fundamental problem in graph analysis and data
mining, aimed at identifying cohesive and densely connected substructures
within a given graph. It plays a crucial role in various domains, including
social network analysis, biological network analysis, recommendation systems,
and community detection. However, extracting a subgraph with the highest node
similarity is a lack of exploration. To address this problem, we studied the
Member Selection Problem and extended it with a dynamic constraint variant. By
incorporating dynamic constraints, our algorithm can adapt to changing
conditions or requirements, allowing for more flexible and personalized
subgraph extraction. This approach enables the algorithm to provide tailored
solutions that meet specific needs, even in scenarios where constraints may
vary over time. We also provide the theoretical analysis to show that our
algorithm is 1/3-approximation. Eventually, the experiments show that our
algorithm is effective and efficient in tackling the member selection problem
with dynamic constraints.
