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Combinatorial Theorems about Embedding Trees on the Real Line
Amit Chakrabarti, Subhash Khot
Dartmouth TR2005-560

Abstract: We consider the combinatorial problem of embedding a tree metric into the real line with low distortion. For two special families of trees --- the family of complete binary trees and the family of subdivided stars --- we provide embeddings whose distortion is provably optimal, up to a constant factor. We also prove that the optimal distortion of a linear embedding of a tree can be arbitrarily low or high even when it has bounded degree.


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   Amit Chakrabarti and Subhash Khot, "Combinatorial Theorems about Embedding Trees on the Real Line." Dartmouth Computer Science Technical Report TR2005-560, October 2005.

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