@TechReport{Dartmouth:TR2005-560,
  author = {Amit Chakrabarti and Subhash Khot},
  title = {{Combinatorial Theorems about Embedding Trees on the Real Line}},
  institution = {Dartmouth College, Computer Science},
  address = {Hanover, NH},
  number = {TR2005-560},
  year = {2005},
  month = {October},
  URL = {http://www.cs.dartmouth.edu/reports/TR2005-560.pdf},
  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.
  }
}