Walking your dog in the woods in polynomial time

Authors:
Erin Wolf Chambers;Éric Colin de Verdière;Jeff Erickson;Sylvain Lazard;Francis Lazarus;Shripad Thite
Affiliations:
UIUC, Urbana, IL, USA;Ecole Normale Supérieure, Paris, France;UIUC, Urbana, IL, USA;INRIA Lorraine, LORIA, Nancy, France;Institut National Polytechnique de Grenoble, Grenoble, France;California Institute of Technology, Pasadena, CA, USA
Venue:
Proceedings of the twenty-fourth annual symposium on Computational geometry
Year:
2008

Citing 10
Cited 5

Slowing down sorting networks to obtain faster sorting algorithms

Journal of the ACM (JACM)
Parallel merge sort

SIAM Journal on Computing
Computing minimum length paths of a given homotopy class

Computational Geometry: Theory and Applications
Polytime algorithm for the shortest path in a homotopy class amidst semi-algebraic obstacles in the plane

ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Applying Parallel Computation Algorithms in the Design of Serial Algorithms

Journal of the ACM (JACM)
An Optimal Algorithm for Euclidean Shortest Paths in the Plane

SIAM Journal on Computing
Computing homotopic shortest paths in the plane

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Parametric search made practical

Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometry—SoCG2002
Computing homotopic shortest paths efficiently

Computational Geometry: Theory and Applications
A theorem on polygon cutting with applications

SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science

Exact algorithms for partial curve matching via the Fréchet distance

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Fréchet Distance Problems in Weighted Regions

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Geodesic Fréchet distance inside a simple polygon

ACM Transactions on Algorithms (TALG)
Link distance and shortest path problems in the plane

Computational Geometry: Theory and Applications
How to walk your dog in the mountains with no magic leash

Proceedings of the twenty-eighth annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 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.