Constant Factor Approximation

Constant factor approximation algorithms aim to find solutions within a guaranteed multiplicative factor of the optimal solution for computationally hard optimization problems. Current research focuses on improving approximation factors for various problems, including submodular maximization (often under knapsack constraints), clustering (with fairness and stability considerations), and robust learning in models like single-index models. These advancements are significant because they provide efficient, provably near-optimal solutions for numerous applications in machine learning, data summarization, and network analysis, where finding exact solutions is intractable.