5 research outputs found

    Walking Through Waypoints

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    We initiate the study of a fundamental combinatorial problem: Given a capacitated graph G=(V,E)G=(V,E), find a shortest walk ("route") from a source s∈Vs\in V to a destination t∈Vt\in V that includes all vertices specified by a set W⊆V\mathscr{W}\subseteq V: the \emph{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

    A Walk in the Clouds:Routing through VNFs on Bidirected Networks

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    Walking Through Waypoints

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    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 finds 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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