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Partitioning points by parallel planes

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

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Identification Number: LSE-CDAM-2002-10

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
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Date Deposited: 16 Dec 2008 16:06
Last Modified: 08 Nov 2012 16:14
URI: http://eprints.lse.ac.uk/id/eprint/13566

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