Low-distortion embeddings of general metrics into the line

A low-distortion embedding between two metric spaces is a mapping which preserves the distances between each pair of points, up to a small factor called distortion. Low-distortion embeddings have recently found numerous applications in computer science. Most of the known embedding results are "absolute", that is, of the form: any metric Y from a given class of metrics C can be embedded into a metric X with low distortion c. This is beneficial if one can guarantee low distortion for all metrics Y in C. However, in many situations, the worst-case distortion is too large to be meaningful. For example, if X is a line metric, then even very simple metrics (an n-point star or an n-point cycle) are embeddable into X only with distortion linear in n. Nevertheless, embeddings into the line (or into low-dimensional spaces) are important for many applications. A solution to this issue is to consider "relative" (or "approximation") embedding problems, where the goal ...

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Mihai Badoiu, Julia Chuzhoy, Piotr Indyk, Anastasios Sidiropoulos
• Keywords: Algorithms, General Metric M, STOC 2005, Weighted Tree, Weighted Tree Metrics