The stretch factor has also been called the distortion[disputed – discuss] or dilation of the mapping.
Research in this area has focused on finding sparse graphs for a given point set that have low stretch factor.
[2] This result, and related methods of constructing low-distortion metric embeddings, are important in the theory of approximation algorithms.
A major open problem in this area is the GNRS conjecture, which (if true) would characterize the families of graphs that have bounded-stretch embeddings into
Undergraduate researcher John Pardon won the 2012 Morgan Prize for his research showing that there is no upper bound on the distortion of torus knots, solving a problem originally posed by Mikhail Gromov.