NDLI: Covering Spheres with Spheres

Content Provider	Springer Nature Link
Author	Dumer, Ilya
Copyright Year	2007
Abstract	Given a sphere of any radius r in an n-dimensional Euclidean space, we study the coverings of this sphere with solid spheres of radius one. Our goal is to design a covering of the lowest covering density, which defines the average number of solid spheres covering a point in a bigger sphere. For growing dimension n, we design a covering that gives the covering density of order (nln n)/2 for a sphere of any radius r>1 and a complete Euclidean space. This new upper bound reduces two times the order nln n established in the classic Rogers bound.
Starting Page	665
Ending Page	679
Page Count	15
File Format	PDF
ISSN	01795376
Journal	Discrete & Computational Geometry
Volume Number	38
Issue Number	4
e-ISSN	14320444
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-09-02
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computational Mathematics and Numerical Analysis Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

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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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Covering Spheres with Spheres