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Lower bounds for the number of hyperplanes separating two finite sets of points

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Abstract

We consider the NP-hard problem of polyhedral separability of two finite sets A and B of points in general position in ℝd by the minimum number of hyperplanes in the sense of a boolean function from a given class Σ. Both deterministic and probabilistic lower bounds are obtained for this number for two different classes of functions Σ.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990, Russia

    K. S. Kobylkin

  2. Graduate School of Economics and Management, Ural Federal University, ul. Mira 19, Yekaterinburg, 620002, Russia

    K. S. Kobylkin

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  1. K. S. Kobylkin
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Correspondence to K. S. Kobylkin.

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Original Russian Text © K.S. Kobylkin, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 2.

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Kobylkin, K.S. Lower bounds for the number of hyperplanes separating two finite sets of points. Proc. Steklov Inst. Math. 289 (Suppl 1), 126–138 (2015). https://doi.org/10.1134/S0081543815050119

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  • DOI: https://doi.org/10.1134/S0081543815050119

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