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This content will become publicly available on July 31, 2024

Title: Metric and Path-Connectedness Properties of the Fréchet Distance for Paths and Graphs
The Fréchet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to hand- writing recognition. More recently, the Fréchet distance has been generalized to a distance between two copies of the same graph embedded or immersed in a metric space; this more general setting opens up a wide range of more complex applications in graph analysis. In this paper, we initiate a study of some of the fundamental topological properties of spaces of paths and of graphs mapped to R^n under the Fréchet distance, in an eort to lay the theoretical groundwork for understanding how these distances can be used in practice. In particular, we prove whether or not these spaces, and the metric balls therein, are path-connected.  more » « less
Award ID(s):
1664858 2046730
NSF-PAR ID:
10485409
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
Proc. Canadian Conference on Computational Geometry
Date Published:
Journal Name:
CCCG
Subject(s) / Keyword(s):
["computational geometry, frechet distance, graphs, metric properties"]
Format(s):
Medium: X
Location:
Montreal, Quebec, Canada
Sponsoring Org:
National Science Foundation
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