How to walk your dog in the mountains with no magic leash

Sariel Har-Peled; Amir Nayyeri; Anastasios Sidiropoulos; Mohammad Salavatipour

doi:10.1145/2261250.2261269

How to walk your dog in the mountains with no magic leash

Sariel Har-Peled, Amir Nayyeri, Anastasios Sidiropoulos, Mohammad Salavatipour

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We describe a O(log n)-approximation algorithm for computing the homotopic Frechét distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms where known only for curves on the Euclidean plane with polygonal obstacles. A key technical ingredient in our analysis is a O(log n)-approximation algorithm for computing the minimum height of a homotopy between two curves. No algorithms were previously known for approximating this parameter. Surprisingly, it is not even known if computing either the homotopic Frechét distance, or the minimum height of a homotopy, is in NP.

Original language	English (US)
Title of host publication	Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012
Pages	121-130
Number of pages	10
DOIs	https://doi.org/10.1145/2261250.2261269
State	Published - Jul 23 2012
Event	28th Annual Symposuim on Computational Geometry, SCG 2012 - Chapel Hill, NC, United States Duration: Jun 17 2012 → Jun 20 2012

Publication series

Name	Proceedings of the Annual Symposium on Computational Geometry

Other

Other	28th Annual Symposuim on Computational Geometry, SCG 2012
Country	United States
City	Chapel Hill, NC
Period	6/17/12 → 6/20/12

Keywords

Approximation algorithms
Frechét distance

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Mathematics

Access to Document

10.1145/2261250.2261269

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Cite this

How to walk your dog in the mountains with no magic leash. / Har-Peled, Sariel; Nayyeri, Amir; Sidiropoulos, Anastasios; Salavatipour, Mohammad.

Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012. 2012. p. 121-130 (Proceedings of the Annual Symposium on Computational Geometry).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Har-Peled, S, Nayyeri, A, Sidiropoulos, A & Salavatipour, M 2012, How to walk your dog in the mountains with no magic leash. in Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012. Proceedings of the Annual Symposium on Computational Geometry, pp. 121-130, 28th Annual Symposuim on Computational Geometry, SCG 2012, Chapel Hill, NC, United States, 6/17/12. https://doi.org/10.1145/2261250.2261269

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