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Link to original content: https://doi.org/10.4230/LIPIcs.SoCG.2021.5
Chasing Puppies: Mobile Beacon Routing on Closed Curves
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Chasing Puppies: Mobile Beacon Routing on Closed Curves

Authors Mikkel Abrahamsen , Jeff Erickson , Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow , Jérôme Urhausen, Jordi Vermeulen, Giovanni Viglietta

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Author Details

Mikkel Abrahamsen
  • BARC, University of Copenhagen, Denmark
Jeff Erickson
  • University of Illinois at Urbana-Champaign, IL, USA
Irina Kostitsyna
  • Eindhoven University of Technology, The Netherlands
Maarten Löffler
  • Utrecht University, The Netherlands
Tillmann Miltzow
  • Utrecht University, The Netherlands
Jérôme Urhausen
  • Utrecht University, The Netherlands
Jordi Vermeulen
  • Utrecht University, The Netherlands
Giovanni Viglietta
  • Japan Advanced Institute of Science and Technology, Nomi City, Ishikawa, Japan

Funding

  • Abrahamsen, Mikkel: Partially supported by the VILLUM Foundation grant 16582.
  • Löffler, Maarten: Partially supported by the Dutch Research Council (NWO) under project number 614.001.504 and 628.011.005.
  • Miltzow, Tillmann: Supported by the Dutch Research Council (NWO) under Veni grant EAGER.
  • Urhausen, Jérôme: Supported by the Dutch Research Council (NWO); 612.001.651.
  • Vermeulen, Jordi: Supported by the Dutch Research Council (NWO); 612.001.651.

Acknowledgements

The authors wish to thank the anonymous reviewers for useful comments and suggestions. Thanks to Ivor van der Hoog, Marc van Kreveld, and Frank Staals for helpful discussions in the early stages of this work, and to Joseph O'Rourke for clarifying the history of the problem. Portions of this work were done while the second author was visiting Utrecht University.

Cite AsGet BibTex

Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, and Giovanni Viglietta. Chasing Puppies: Mobile Beacon Routing on Closed Curves. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.SoCG.2021.5

Abstract

We solve an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others’ work on beacon-based routing. Consider a human and a puppy on a simple closed curve in the plane. The human can walk along the curve at bounded speed and change direction as desired. The puppy runs with unbounded speed along the curve as long as the Euclidean straight-line distance to the human is decreasing, so that it is always at a point on the curve where the distance is locally minimal. Assuming that the curve is smooth (with some mild genericity constraints) or a simple polygon, we prove that the human can always catch the puppy in finite time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Beacon routing
  • navigation
  • generic smooth curves
  • puppies

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References

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