Partitioning points by parallel planes
Anthony, M.
(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.
(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.
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.