On the 3-distortion of a path (Q2462328)

This paper deals with the metric distortion of an embedding of a metric space into Euclidean space. In particular the 3-distortion takes into account 3-tuples of points rather than just pairs. It is proved that the 3-distortion is \(\Omega(n^{1/2})\) in the plane, and it is \(\Omega(n^{1/(d-1)})\) in \(d\)-space, if \(n\) denotes the length of a path. This is of importance in algorithmic geometry and its applications.