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Low-distortion embeddings of general metrics into the line

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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 ...
Mihai Badoiu, Julia Chuzhoy, Piotr Indyk, Anastasi
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2005
Where STOC
Authors Mihai Badoiu, Julia Chuzhoy, Piotr Indyk, Anastasios Sidiropoulos
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