\Tilde{o}$ Query

The field of query complexity investigates the minimum number of queries needed to solve computational problems, focusing on the trade-off between query efficiency and memory usage. Current research emphasizes the analysis of gradient descent and cutting-plane methods within various problem settings, including feasibility problems, convex optimization, and submodular maximization, to determine their optimality in this trade-off. These studies reveal sharp phase transitions in computational complexity based on memory constraints, highlighting the fundamental limits of efficient algorithms. Understanding these trade-offs is crucial for designing efficient algorithms in machine learning and other areas where large-scale datasets are common.