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[Colloquium] Walking Your Dog in the Woods in Polynomial Time

March 27, 2008

Watch Colloquium: 

  • Date: Thursday, March 27th, 2008 
  • Time: 11 am — 12:15 pm 
  • Place: ME 218

Shripad Thite
Center for the Mathematics of Information 

The Frechet 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 Frechet 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 point obstacles (‘trees’). Thus, we introduce the homotopic Frechet distance between two curves embedded in a general metric space. We describe a polynomial-time algorithm to compute the homotopic Frechet distance between two given polygonal curves in the plane minus a given set of obstacles, which are either points or polygons.

This is joint work with Erin Wolf Chambers, Eric Colin de Verdiere, Jeff Erickson, Sylvain Lazard, and Francis Lazarus, to appear at SoCG’08 and invited to a CGTA special issue.