Walking through waypoints

Abstract

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 W⊆ V: the waypoints. This waypoint routing problem finds immediate applications in the context of modern networked distributed 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.