## Abstract

The doubling constant of a metric space (X, d) is the smallest value λ such that every ball in X can be covered by λ balls of half the radius. The doubling dimension of X is then defined as dim(X) = log_{2} λ. A metric (or sequence of metrics) is called doubling precisely when its doubling dimension is bounded. This is a robust class of metric spaces which contains many families of metrics that occur in applied settings. We give tight bounds for embedding doubling metrics into (low-dimensional) normed spaces. We consider both general doubling metrics, as well as more restricted families such as those arising from trees, from graphs excluding a fixed minor, and from snowflaked metrics. Our techniques include decomposition theorems for doubling metrics, and an analysis of a fractal in the plane due to Laakso [21]. Finally, we discuss some applications and point out a central open question regarding dimensionality reduction in L_{2}.

Original language | English (US) |
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Pages (from-to) | 534-543 |

Number of pages | 10 |

Journal | Annual Symposium on Foundations of Computer Science - Proceedings |

State | Published - 2003 |

Event | Proceedings: 44th Annual IEEE Symposium on Foundations of Computer Science - FOCS 2003 - Cambridge, MA, United States Duration: Oct 11 2003 → Oct 14 2003 |

## ASJC Scopus subject areas

- Hardware and Architecture
- General Computer Science