Partitioning points by parallel planes

Anthony, Martin ORCID: 0000-0002-7796-6044 (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
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	16 Dec 2008 16:06
Last Modified:	12 Dec 2024 05:39
URI:	http://eprints.lse.ac.uk/id/eprint/13566

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