@inproceedings{df67b834cedc4ce38dac85520a0ce2d5,
title = "On the impossibility of dimension reduction for doubling subsets of ℓp",
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 ℓp spaces with p > 2. In particular, we introduce an n-point subset of ℓp with doubling constant O(1), and demonstrate that any embedding of the set into ℓpd with distortion D must have D ≥ Ω ((c log n/d 1/2-1/p Copyright is held by the owner/author(s).",
keywords = "Dimension reduction, Doubling metrics, Embedding",
author = "Yair Bartal and Gottlieb, \{Lee Ad\} and Ofer Neiman",
year = "2014",
month = jan,
day = "1",
doi = "10.1145/2582112.2582170",
language = "English",
isbn = "9781450325943",
series = "Proceedings of the Annual Symposium on Computational Geometry",
publisher = "Association for Computing Machinery",
pages = "60--66",
booktitle = "Proceedings of the 30th Annual Symposium on Computational Geometry, SoCG 2014",
note = "30th Annual Symposium on Computational Geometry, SoCG 2014 ; Conference date: 08-06-2014 Through 11-06-2014",
}