Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation

Understand

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.