NDLI: Bounded geometries, fractals, and low-distortion embeddings

Content Provider	IEEE Xplore Digital Library
Author	Gupta, A. Krauthgamer, R. Lee, J.R.
Copyright Year	2003
Description	Author affiliation: Dept. of Comput. Sci., Carnegie Mellon Univ., Pittsburgh, PA, USA (Gupta, A.)
Abstract	The doubling constant of a metric space (X, d) is the smallest value /spl lambda/ such that every ball in X can be covered by /spl lambda/ balls of half the radius. The doubling dimension of X is then defined as dim (X) = log/sub 2//spl lambda/. 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 according to T. J. Laakso (2002). Finally, we discuss some applications and point out a central open question regarding dimensionality reduction in L/sub 2/.
Sponsorship	IEEE Comput. Soc. Tech. Soc. on Found. Comput
Starting Page	534
Ending Page	543
File Size	396081
Page Count	10
File Format	PDF
ISBN	0769520405
ISSN	02725428
DOI	10.1109/SFCS.2003.1238226
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-10-11
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Extraterrestrial measurements Computer science Tree graphs Geometry Robustness Fractals Algorithm design and analysis Combinatorial mathematics Power generation Graph theory
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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