Trees and Markov convexity

James R. Lee, Assaf Naor, Yuval Peres

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We give combinatorial, geometric, and probabilistic characterizations of the distortion of tree metrics into Lp spaces. This requires the development of new embedding techniques, as well as a method for proving distortion lower bounds which is based on the wandering of Markov chains in Banach spaces, and a new metric invariant we call Markov convexity. Trees are thus the first non-trivial class of metric spaces for which one can give a simple and complete characterization of their distortion into a Hubert space, up to universal constants. Our results also yield an efficient algorithm for constructing such embeddings.

Original languageEnglish (US)
Title of host publicationProceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
Pages1028-1037
Number of pages10
StatePublished - 2006
EventSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States
Duration: Jan 22 2006Jan 24 2006

Other

OtherSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
CountryUnited States
CityMiami, FL
Period1/22/061/24/06

Fingerprint

Convexity
Invariant Metric
Hubert Space
Banach spaces
Lp Spaces
Markov processes
Metric space
Markov chain
Efficient Algorithms
Banach space
Lower bound
Metric
Class

ASJC Scopus subject areas

  • Software
  • Discrete Mathematics and Combinatorics
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

Cite this

Lee, J. R., Naor, A., & Peres, Y. (2006). Trees and Markov convexity. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1028-1037)

Trees and Markov convexity. / Lee, James R.; Naor, Assaf; Peres, Yuval.

Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. 2006. p. 1028-1037.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lee, JR, Naor, A & Peres, Y 2006, Trees and Markov convexity. in Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 1028-1037, Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, United States, 1/22/06.
Lee JR, Naor A, Peres Y. Trees and Markov convexity. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. 2006. p. 1028-1037
Lee, James R. ; Naor, Assaf ; Peres, Yuval. / Trees and Markov convexity. Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. 2006. pp. 1028-1037
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