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Partitioning points by parallel planes

Anthony, Martin (2002) Partitioning points by parallel planes. CDAM research report series, LSE-CDAM-2002-10. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

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Abstract

A new upper bound is given on the number of ways in which a set of N points in Rn can be partitioned by k parallel hyperplanes. This bound improves upon a result of Olafsson and Abu-Mostafa [IEEE Trans. Pattern Analysis and Machine Intelligence 10(2), 1988: 277-281]; it agrees with the known (tight) result for the case k = 1; and it is, for fixed k and n, tight to within a constant. A previously published claimed improvement to the bound of Olafsson and Abu-Mostafa is shown to be incorrect.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk
Additional Information: © 2002 the author
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2002-10
Date Deposited: 16 Dec 2008 16:06
URL: http://eprints.lse.ac.uk/13566/

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