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Partitioning points by parallel planes

By Martin Anthony

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

Topics: QA Mathematics
Publisher: Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science
Year: 2002
OAI identifier: oai:eprints.lse.ac.uk:13566
Provided by: LSE Research Online
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