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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 2, Pages 210–222 (Mi timm1070)  
This article is cited in 4 scientific papers (total in 4 papers)

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

K. S. Kobylkinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b B. N. Yeltsin Ural Federal University
Full-text PDF (233 kB) Citations (4)
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Abstract: We consider the $NP$-hard polyhedral separability problem for two subsets $A$ and $B$ of points in general position in $\mathbb R^d$ with the fewest number of hyperplanes in the sense of boolean functions from a given class $\Sigma$. Both deterministic and probabilistic lower bounds are obtained for this number for two different classes of functions $\Sigma$.
Keywords: $k$-polyhedral separability, boolean function, monochromatic island, combinatorial discrepancy.
Received: 06.03.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 289, Issue 1, Pages 126–138
DOI: https://doi.org/10.1134/S0081543815050119
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: K. S. Kobylkin, “Lower bounds for the number of hyperplanes separating two finite sets of points”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 2, 2014, 210–222; Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), 126–138
Citation in format AMSBIB
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\paper Lower bounds for the number of hyperplanes separating two finite sets of points
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 2
\pages 210--222
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 289
\issue , suppl. 1
\pages 126--138
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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