Paper by Erik D. Demaine
- Noga Alon, Mihai Bădoiu, Erik D. Demaine, Martin Farach-Colton, MohammadTaghi Hajiaghayi, and Anastasios Sidiropoulos, “Ordinal Embeddings of Minimum Relaxation: General Properties, Trees, and Ultrametrics”, in Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), Vancouver, British Columbia, Canada, January 23–25, 2005, pages 650–659.
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.
- The paper is 10 pages.
- The paper is available in PostScript (344k), gzipped PostScript (128k), and PDF (192k).
- See information on file formats.
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- Related papers:
- Ordinal_TAlg (Ordinal Embeddings of Minimum Relaxation: General Properties, Trees, and Ultrametrics)
- Ordinal_APPROX2008 (Ordinal Embedding: Approximation Algorithms and Dimensionality Reduction)
See also other papers by Erik Demaine.
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