Solving maximum flow problems on real-world bipartite graphs

In this article, we present an experimental study of several maximum-flow algorithms in the context of unbalanced bipartite networks. Our experiments are motivated by a real-world problem of managing reservation-based inventory in Google content ad systems. We are interested in observing the performance of several push-relabel algorithms on our real-world datasets and also on some generated ones. Previous work suggested an important improvement for push-relabel algorithms on unbalanced bipartite networks: the two-edge push rule. We show how the two-edge push rule improves the running time. While no single algorithm dominates the results, we show there is one that has very robust performance in practice.