Median Problem

The median problem, encompassing variations like k-medians and p-medians, seeks to optimize the location of facilities (e.g., bike stations, logistics hubs) to minimize the aggregate distance to clients. Current research focuses on developing efficient algorithms, including integer programming, memetic optimization, metaheuristics (genetic algorithms, simulated annealing), and deep reinforcement learning, to solve these often NP-hard problems, particularly in constrained settings like fair clustering and those involving graph structures. These advancements are crucial for applications ranging from urban planning and logistics to data analysis and machine learning, improving resource allocation and fairness in various domains. Furthermore, research explores coreset constructions and approximation algorithms to handle large datasets efficiently while preserving solution quality.