A column generation approach to the discrete barycenter problem

The discrete Wasserstein barycenter problem is a minimum-cost mass transport for set of probability measures. Although an exact computable through linear programming, the underlying program can be extremely large. For worst-case input, best known programming formulation exponential in number variables, but has low constraints, making it interesting candidate column generation. In this paper, we devise and study two generation strategies: natural one based on simplified computation reduced costs, Dantzig–Wolfe decomposition. latter, produce efficiently solvable subproblems, namely, pricing form classical transportation problem. strategies begin with efficient initial feasible solution. While structure constraints leads to costs all remaining variables setup, both approaches may outperform using full speed, dramatically so memory requirement. our computational experiments, exhibit that, depending either strategy become choice.