Embedding tree metrics into low-dimensional Euclidean spaces

A. Gupta

Research output: Contribution to journalArticlepeer-review


We consider embedding metrics induced by trees into Euclidean spaces with a restricted number of dimensions. We show that any weighted tree T with n vertices and L leaves can be embedded into d-dimensional Euclidean space with Õ (L1/(d-1)) distortion. Furthermore, we exhibit an embedding with almost the same distortion which can be computed efficiently. This distortion substantially improves the previous best upper bound of Õ (n2/d) and almost matches the best known lower bound of Ω (L1/d).

Original languageEnglish (US)
Pages (from-to)105-116
Number of pages12
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Jul 2000

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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