Chasing Puppies: Mobile Beacon Routing on Closed Curves

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 well-behaved, we prove that the human can always catch the puppy in finite time, using a simple (but not quite trivial) strategy.

Conference Proceedings (peer-reviewed)

Archived Publication (not reviewed)

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