Geodesic Fréchet Distance Inside a Simple Polygon - Archive ouverte HAL Access content directly
Conference Papers Year : 2008

Geodesic Fréchet Distance Inside a Simple Polygon

Abstract

We unveil an alluring alternative to parametric search that applies to both the non-geodesic and geodesic Fréchet optimization problems. This randomized approach is based on a variant of red-blue intersections and is appealing due to its elegance and practical efficiency when compared to parametric search. We present the first algorithm for the geodesic Fréchet distance between two polygonal curves $A$ and $B$ inside a simple bounding polygon $P$. The geodesic Fréchet decision problem is solved almost as fast as its non-geodesic sibling and requires $O(N^{2\log k)$ time and $O(k+N)$ space after $O(k)$ preprocessing, where $N$ is the larger of the complexities of $A$ and $B$ and $k$ is the complexity of $P$. The geodesic Fréchet optimization problem is solved by a randomized approach in $O(k+N^{2\log kN\log N)$ expected time and $O(k+N^{2)$ space. This runtime is only a logarithmic factor larger than the standard non-geodesic Fréchet algorithm (Alt and Godau 1995). Results are also presented for the geodesic Fréchet distance in a polygonal domain with obstacles and the geodesic Hausdorff distance for sets of points or sets of line segments inside a simple polygon $P$.
Fichier principal
Vignette du fichier
Cook.pdf (249.01 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00221494 , version 1 (28-01-2008)

Identifiers

Cite

Atlas F. Cook Iv, Carola Wenk. Geodesic Fréchet Distance Inside a Simple Polygon. STACS 2008, Feb 2008, Bordeaux, France. pp.193-204. ⟨hal-00221494⟩

Collections

STACS2008
57 View
531 Download

Altmetric

Share

Gmail Facebook X LinkedIn More