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.
|Title of host publication||37th International Symposium on Computational Geometry, SoCG 2021|
|Editors||Kevin Buchin, Eric Colin de Verdiere|
|Publisher||Schloss Dagstuhl - Leibniz-Zentrum für Informatik|
|Publication status||Published - 1 Jun 2021|
|Event||37th International Symposium on Computational Geometry, SoCG 2021 - Virtual, Buffalo, United States|
Duration: 7 Jun 2021 → 11 Jun 2021
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||37th International Symposium on Computational Geometry, SoCG 2021|
|Period||7/06/21 → 11/06/21|
Bibliographical noteFunding Information:
Funding Mikkel Abrahamsen: Partially supported by the VILLUM Foundation grant 16582. Maarten Löffler: Partially supported by the Dutch Research Council (NWO) under project number 614.001.504 and 628.011.005. Tillmann Miltzow: Supported by the Dutch Research Council (NWO) under Veni grant EAGER. Jérôme Urhausen: Supported by the Dutch Research Council (NWO); 612.001.651. Jordi Vermeulen: Supported by the Dutch Research Council (NWO); 612.001.651.
© Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, and Giovanni Viglietta; licensed under Creative Commons License CC-BY 4.0 37th International Symposium on Computational Geometry (SoCG 2021).
- Beacon routing
- Generic smooth curves