Clustering for set partitioning with a case study in ridesharing

By exploring alternative approaches to combinatorial optimization, we propose the first known formal connection between clustering and set partitioning, with the goal of identifying a subclass of set partitioning problems that can be solved efficiently and with optimality guarantees through a clustering approach. We prove the equivalence between classical centroid clustering problems and a special case of set partitioning called metric k-set partitioning. We discuss the implications for k-means and regularized geometric k-medians, and we give several future extensions and applications. Finally, we present a case study in combinatorial optimization for ridesharing, in which we use an efficient Expectation Maximization (EM) style algorithm to achieve a 69% reduction in total vehicle distance, as compared with no ridesharing.