Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set

Jean Daniel Boissonnat; Kunal Dutta; Arijit Ghosh; Sudeshna Kolay

doi:10.1007/978-3-319-77404-6_15

Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set

Jean Daniel Boissonnat, Kunal Dutta, Arijit Ghosh, Sudeshna Kolay

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

The Point Hyperplane Cover problem in ℝ^d takes as input a set of n points in 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 ℝ^d takes as input a family F of D-degree polynomials from a vector space R in ℝ^d, and determines whether there is a set of at most k points in ℝ^d that hit all the polynomials in F. For both problems, we exhibit tight kernels where k is the parameter.

Original language	English
Title of host publication	LATIN 2018
Subtitle of host publication	Theoretical Informatics - 13th Latin American Symposium, Proceedings
Editors	Miguel A. Mosteiro, Michael A. Bender, Martin Farach-Colton
Publisher	Springer Verlag
Pages	187-200
Number of pages	14
ISBN (Print)	9783319774039
DOIs	https://doi.org/10.1007/978-3-319-77404-6_15
State	Published - 1 Jan 2018
Externally published	Yes
Event	13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 - Buenos Aires, Argentina Duration: 16 Apr 2018 → 19 Apr 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10807 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Symposium on Latin American Theoretical Informatics, LATIN 2018
Country/Territory	Argentina
City	Buenos Aires
Period	16/04/18 → 19/04/18

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-77404-6_15

Cite this

Boissonnat, J. D., Dutta, K., Ghosh, A., & Kolay, S. (2018). Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set. In M. A. Mosteiro, M. A. Bender, & M. Farach-Colton (Eds.), LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings (pp. 187-200). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10807 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-77404-6_15

Boissonnat, Jean Daniel ; Dutta, Kunal ; Ghosh, Arijit et al. / Tight kernels for covering and hitting : Point hyperplane cover and polynomial point hitting set. LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. editor / Miguel A. Mosteiro ; Michael A. Bender ; Martin Farach-Colton. Springer Verlag, 2018. pp. 187-200 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The Point Hyperplane Cover problem in ℝd takes as input a set of n points in ℝd 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 ℝd takes as input a family F of D-degree polynomials from a vector space R in ℝd, and determines whether there is a set of at most k points in ℝd that hit all the polynomials in F. For both problems, we exhibit tight kernels where k is the parameter.",

author = "Boissonnat, {Jean Daniel} and Kunal Dutta and Arijit Ghosh and Sudeshna Kolay",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 ; Conference date: 16-04-2018 Through 19-04-2018",

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Boissonnat, JD, Dutta, K, Ghosh, A & Kolay, S 2018, Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set. in MA Mosteiro, MA Bender & M Farach-Colton (eds), LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10807 LNCS, Springer Verlag, pp. 187-200, 13th International Symposium on Latin American Theoretical Informatics, LATIN 2018, Buenos Aires, Argentina, 16/04/18. https://doi.org/10.1007/978-3-319-77404-6_15

Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set. / Boissonnat, Jean Daniel; Dutta, Kunal; Ghosh, Arijit et al.
LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. ed. / Miguel A. Mosteiro; Michael A. Bender; Martin Farach-Colton. Springer Verlag, 2018. p. 187-200 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10807 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The Point Hyperplane Cover problem in ℝd takes as input a set of n points in ℝd 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 ℝd takes as input a family F of D-degree polynomials from a vector space R in ℝd, and determines whether there is a set of at most k points in ℝd that hit all the polynomials in F. For both problems, we exhibit tight kernels where k is the parameter.

AB - The Point Hyperplane Cover problem in ℝd takes as input a set of n points in ℝd 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 ℝd takes as input a family F of D-degree polynomials from a vector space R in ℝd, and determines whether there is a set of at most k points in ℝd that hit all the polynomials in F. For both problems, we exhibit tight kernels where k is the parameter.

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Boissonnat JD, Dutta K, Ghosh A, Kolay S. Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set. In Mosteiro MA, Bender MA, Farach-Colton M, editors, LATIN 2018: Theoretical Informatics - 13th Latin American Symposium, Proceedings. Springer Verlag. 2018. p. 187-200. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-77404-6_15

Tight kernels for covering and hitting: Point hyperplane cover and polynomial point hitting set

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