A Polyhedral Approach to Online Bipartite Matching

We study the i.i.d. online bipartite matching problem, a dynamic version of the classical model where one side of the bipartition is fixed and known in advance, while nodes from the other side appear one at a time as i.i.d. realizations of an underlying distribution, and must immediately be matched or discarded. We consider various relaxations of the set of achievable matching probabilities, introduce star inequalities and their generalizations, and discuss when they are facet-defining. We also show how several of these relaxations correspond to ranking policies and their time-dependent generalizations. We finally present results of a computational study of these relaxations and policies to determine their empirical performance.