| M. Anthony. Partitioning points by parallel planes. RUTCOR Research Report RRR39 -2002, Rutgers Center for Operations Research, 2002. (Also, CDAM research report LSE-CDAM-2002-10, Centre for Discrete and Applicable Mathematics, London School of Economics.) |
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M. Anthony. Partitioning points by parallel planes. RUTCOR Research Report RRR39 -2002, Rutgers Center for Operations Research, 2002. (Also, CDAM research report LSE-CDAM-2002-10, Centre for Discrete and Applicable Mathematics, London School of Economics.)
....lists is to use this fact in combination with some known bounds [8, 4] for the growth functions of linear threshold networks. This gives a similar, though slightly looser, upper bound. To bound the growth function of the subclass consisting of s level threshold functions, we use a result from [1], which shows that the number of ways in which a set S of m points can be partitioned by s parallel hyperplanes is at most : For fixed n and s, this bound is 10 tight to within a constant, as a function of m. Noting that we may assume adjacent regions to have different labels, there ....
M. Anthony. Partitioning points by parallel planes. RUTCOR Research Report RRR39 -2002, Rutgers Center for Operations Research. (Also, CDAM research report LSECDAM -2002-10, Centre for Discrete and Applicable Mathematics, London School of Economics.)
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