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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
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
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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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