Chasing Puppies: Mobile Beacon Routing on Closed Curves
Publication date
2021-06-01
Authors
Miltzow, Till
Abrahamsen, Mikkel
Erickson, Jeff
Kostitsyna, Irina
Urhausen, Jérôme
Vermeulen, Jordi
Viglietta, Giovanni
Editors
Advisors
Supervisors
Document Type
Contribution to conference
Metadata
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License
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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.
Keywords
Beacon routing, Generic smooth curves, Navigation, Puppies, Software
Citation
Miltzow, T, Abrahamsen, M, Erickson, J, Kostitsyna, I, Urhausen, J, Vermeulen, J & Viglietta, G 2021, 'Chasing Puppies: Mobile Beacon Routing on Closed Curves', Paper presented at 37th International Symposium on Computational Geometry , 7/07/21 - 11/07/21 pp. 5:1-5:19. https://doi.org/10.4230/LIPIcs.SoCG.2021.5, conference