Walking Through Waypoints

  • Saeed Akhoondian Amiri
  • Klaus-Tycho FoersterEmail author
  • Stefan Schmid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10807)


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


Waypoint Short Walk Nice Tree Decomposition Bounded Treewidth Graphs Edge-disjoint Paths Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors would like to thank Riko Jacob for helpful discussions and feedback. Klaus-Tycho Foerster’s and Stefan Schmid’s research was partly supported by the Villum project ReNet and by Aalborg University’s PreLytics project. Saeed Amiri’s research was partly supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 648527).


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.TU Berlin and Max Planck Institute for Informatics (Saarland)SaarbrückenGermany
  2. 2.University of ViennaViennaAustria

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