Technical Report Number
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.
Dartmouth Digital Commons Citation
Chakrabarti, Amit and Khot, Subhash, "Combinatorial Theorems about Embedding Trees on the Real Line" (2005). Computer Science Technical Report TR2005-560. https://digitalcommons.dartmouth.edu/cs_tr/281