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Tight Kernels for Covering and Hitting: Point Hyperplane Cover and Polynomial Point Hitting Set

  • Jean-Daniel Boissonnat
  • Kunal Dutta
  • Arijit Ghosh
  • Sudeshna Kolay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10807)

Abstract

The Point Hyperplane Cover problem in \(\mathbb {R}^d\) takes as input a set of n points in \(\mathbb {R}^d\) and a positive integer k. The objective is to cover all the given points with a set of at most k hyperplanes. The D-Polynomial Points Hitting Set (D-Polynomial Points HS) problem in \(\mathbb {R}^d\) takes as input a family \(\mathcal {F}\) of D-degree polynomials from a vector space \(\mathcal {R}\) in \(\mathbb {R}^d\), and determines whether there is a set of at most k points in \(\mathbb {R}^d\) that hit all the polynomials in \(\mathcal {F}\). For both problems, we exhibit tight kernels where k is the parameter.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jean-Daniel Boissonnat
    • 1
  • Kunal Dutta
    • 1
  • Arijit Ghosh
    • 2
  • Sudeshna Kolay
    • 3
  1. 1.Université Côte d’Azur, InriaSophia AntipolisFrance
  2. 2.Indian Statistical InstituteKolkataIndia
  3. 3.Eindhoven University of TechnologyEindhovenNetherlands

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