Walking your dog in the woods in polynomial time

Written with Erin Wolf Chambers*, Éric Colin de Verdière, Sylvain Lazard, Francis Lazarus, and Shripad Thite.

Computational Geometry: Theory and Applications 43(3):295–311, 2010.
(Special issue of invited papers from the 24th Annual Symposium on Computational Geometry)
My final contribution to Elsevier. (Here are some reasons.)

Proceedings of the 24th Annual ACM Symposium on Computational Geometry, 101–109, 2008.

The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking. We propose a natural extension of Fréchet distance to more general metric spaces, which requires the leash itself to move continuously over time. For example, for curves in the punctured plane, the leash cannot pass through or jump over the point obstacles ("trees"). We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of obstacles, which are either points or polygons.

Publications - Jeff Erickson (jeffe@cs.uiuc.edu) 21 Jan 2012