We initiate the study of a fundamental combinatorial problem: Given a capacitated graph G = (V, E), find a shortest walk (“route”) from a source s ∈ V to a destination t ∈ V that includes all vertices specified by a set WP ⊆ V: the waypoints. This Waypoint Routing Problem fnds immediate applications in the context of modern networked systems. Our main contribution is an exact polynomial-time algorithm for graphs of bounded treewidth. We also show that if the number of waypoints is logarithmically bounded, exact polynomial-time algorithms exist even for general graphs. Our two algorithms provide an almost complete characterization of what can be solved exactly in polynomial time: we show that more general problems (e.g., on grid graphs of maximum degree 3, with slightly more waypoints) are computationally intractable.

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