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Multi-user routing to single destination with confluence

The recent increase in attention to ride-sharing applications demonstrates the importance of routing algorithms for multiple users who obtain benefits from confluence, that is, traveling together on all or part of their routes. We propose novel and flexible formulation of routing optimization for multiple users who have their respective sources and a single common destination. The formulation is general enough to express each user's benefit (or cost) of confluence for every combination of users. Hence, the formulation can represent a wide range of applications and subsumes almost all formulations proposed in literature. We establish an efficient exact method for the formulation. Interestingly, we found well-known Dreyfus-Wagner Algorithm for the Minimum Steiner Tree Problem (MSTP) is extensible for ours, although our formulation is much harder than the MSTP. Our experimental results obtained on large-scale road networks reveal that our method is efficient in practical settings.