Theoretical Background
Indyk et al proved the following theorems in Approximation Algorithms
for Embeddings Into Low-Dimensional Spaces. They provide an upper bound
on the maximum distortion for any data set of points on S2
that is then embedded into the plane. The actual proof can be obtained
from the paper.
Worst Case Upper Bound
Worst Case Lower Bound
A 3.512-Approximation
Algorithm Under the Euclidean Distance
