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 that Bernstein et al. (2000) , developed in the context of manifold learning, and those of Karaman and Frazzoli (2011), developed in the context of robotics . We do the same with curvature-constrained shortest paths and their distances, establishing what we believe are the first approximation bounds for them.
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.
R
that
of
D
, developed in the context of manifold learning, and those of Karaman and Frazzoli (2011), developed in the context of robotics