@inproceedings{74aea967493d40bcbcb163b224616cde,
title = "Walking your dog in the woods in polynomial time",
abstract = "The Fr{\'e}chet 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 Fr{\'e}chet 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 obstacles ({"}trees{"}). We describe a polynomial-time algorithm to compute the homotopic Fr{\'e}chet distance between two given polygonal curves in the plane minus a given set of obstacles, which are either points or polygons.",
keywords = "Geodesic leash map, Homotopic fr{\'e}chet distance",
author = "Chambers, \{Erin Wolf\} and \{De Verdi{\`e}re\}, \{{\'E}ric Colin\} and Jeff Erickson and Bylvain Lazard and Francis Lazarus and Shripad Ihite",
year = "2008",
doi = "10.1145/1377676.1377694",
language = "English (US)",
isbn = "9781605580715",
series = "Proceedings of the Annual Symposium on Computational Geometry",
publisher = "Association for Computing Machinery",
pages = "101--109",
booktitle = "Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08",
address = "United States",
note = "24th Annual Symposium on Computational Geometry, SCG'08 ; Conference date: 09-06-2008 Through 11-06-2008",
}