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TALG
2008

Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics

8 years 9 months ago
Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics
We introduce a new notion of embedding, called minimum-relaxation ordinal embedding, parallel to the standard notion of minimum-distortion (metric) embedding. In an ordinal embedding, it is the relative order between pairs of distances, and not the distances themselves, that must be preserved as much as possible. The (multiplicative) relaxation of an ordinal embedding is the maximum ratio between two distances whose relative order is inverted by the embedding. We develop several worst-case bounds and approximation algorithms on ordinal embedding. In particular, we establish that ordinal embedding has many qualitative differences from metric embedding, and capture the ordinal behavior of ultrametrics and shortest-path metrics of unweighted trees.
Noga Alon, Mihai Badoiu, Erik D. Demaine, Martin F
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TALG
Authors Noga Alon, Mihai Badoiu, Erik D. Demaine, Martin Farach-Colton, Mohammad Taghi Hajiaghayi, Anastasios Sidiropoulos
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