### Abstract

We give combinatorial, geometric, and probabilistic characterizations of the distortion of tree metrics into L_{p} 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 language | English (US) |
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Title of host publication | Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 1028-1037 |

Number of pages | 10 |

State | Published - 2006 |

Event | Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States Duration: Jan 22 2006 → Jan 24 2006 |

### Other

Other | Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | Miami, FL |

Period | 1/22/06 → 1/24/06 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Trees and Markov convexity

AU - Lee, James R.

AU - Naor, Assaf

AU - Peres, Yuval

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33244484172&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33244484172&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33244484172

SP - 1028

EP - 1037

BT - Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms

ER -