Cardinality Constraint

Cardinality constraints, which limit the number of selected elements in an optimization problem, are central to many machine learning and data mining tasks, aiming to find optimal solutions while maintaining sparsity or interpretability. Current research focuses on developing efficient algorithms for submodular maximization under cardinality constraints, exploring both theoretical approximation guarantees and practical performance, often employing techniques like iterative hard thresholding, SDP relaxations, and streaming algorithms. These advancements are crucial for addressing challenges in diverse applications, including feature selection, counterfactual explanation generation, and fair resource allocation, where balancing solution quality with constraint satisfaction is paramount.