## Abstract

A major open problem in the field of metric embedding is the existence of dimension reduction for n-point subsets of Euclidean space, such that both distortion and dimension depend only on the doubling constant of the pointset, and not on its cardinality. In this paper, we negate this possibility for ℓ_{p} spaces with p > 2. In particular, we introduce an n-point subset of ℓ_{p} with doubling constant O(1), and demonstrate that any embedding of the set into ℓ_{p}^{d} with distortion D must have D ≥ Ω ((c log n/d ^{1/2-1/p} Copyright is held by the owner/author(s).

Original language | English |
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Title of host publication | Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014 |

Publisher | Association for Computing Machinery |

Pages | 60-66 |

Number of pages | 7 |

ISBN (Print) | 9781450325943 |

DOIs | |

State | Published - 1 Jan 2014 |

Event | 30th Annual Symposium on Computational Geometry, SoCG 2014 - Kyoto, Japan Duration: 8 Jun 2014 → 11 Jun 2014 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Conference

Conference | 30th Annual Symposium on Computational Geometry, SoCG 2014 |
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Country/Territory | Japan |

City | Kyoto |

Period | 8/06/14 → 11/06/14 |

## Keywords

- Dimension reduction
- Doubling metrics
- Embedding

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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