Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation
Computational Geometry
2018-10-26 v2 Metric Geometry
Abstract
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of Bernstein et al. (2000). We do the same with curvature-constrained shortest paths and their distances, establishing what we believe are the first approximation bounds for them.
Cite
@article{arxiv.1706.09441,
title = {Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation},
author = {Ery Arias-Castro and Thibaut Le Gouic},
journal= {arXiv preprint arXiv:1706.09441},
year = {2018}
}