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Walking Through Waypoints

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LATIN 2018: Theoretical Informatics (LATIN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10807))

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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 \(s\in V\) 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.

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Notes

  1. 1.

    A preliminary full version is provided at [3].

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Acknowledgments

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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Authors and Affiliations

  1. TU Berlin and Max Planck Institute for Informatics (Saarland), Saarbrücken, Germany

    Saeed Akhoondian Amiri

  2. University of Vienna, Vienna, Austria

    Klaus-Tycho Foerster & Stefan Schmid

Authors
  1. Saeed Akhoondian Amiri
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  2. Klaus-Tycho Foerster
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  3. Stefan Schmid
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Correspondence to Klaus-Tycho Foerster .

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Editors and Affiliations

  1. Stony Brook University, Stony Brook, New York, USA

    Michael A. Bender

  2. Rutgers University, New Brunswick, New Jersey, USA

    Martín Farach-Colton

  3. Pace University, New York, New York, USA

    Miguel A. Mosteiro

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Akhoondian Amiri, S., Foerster, KT., Schmid, S. (2018). Walking Through Waypoints. In: Bender, M., Farach-Colton, M., Mosteiro, M. (eds) LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science(), vol 10807. Springer, Cham. https://doi.org/10.1007/978-3-319-77404-6_4

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