Chasing Puppies: Mobile Beacon Routing on Closed Curves

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

arXiv · 2103.09811

Chasing Puppies: Mobile Beacon Routing on Closed Curves

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

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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.

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Mikkel Abrahamsen, Jeff Erickson, Irina Kostitsyna, Maarten Löffler, Tillmann Miltzow, Jérôme Urhausen, Jordi Vermeulen, Giovanni Viglietta. 2021-03-17. Chasing Puppies: Mobile Beacon Routing on Closed Curves. https://arxiv.org/abs/2103.09811

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