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

##### Ery Arias-Castro, Thibaut Le Gouic

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.

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