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

Algorithms, Geometry and Applications

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

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: Theoretical Informatics
Subtitle of host publication	13th Latin American Symposium, Buenos Aires, Argentina, April 16-19, 2018, Proceedings
Editors	M.A. Bender, M. Farach-Colton, M.A. Mosteiro
Place of Publication	Dordrecht
Publisher	Springer
Pages	187-200
Number of pages	14
ISBN (Electronic)	978-3-319-77404-6
ISBN (Print)	978-3-319-77403-9
DOIs	https://doi.org/10.1007/978-3-319-77404-6_15
Publication status	Published - 1 Jan 2018
Event	13th Latin American Theoretical INformatics Symposium (LATIN 2018) - Buenos Aires, Argentina Duration: 16 Apr 2018 → 19 Apr 2018 Conference number: 13 http://latin2018.dc.uba.ar/

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 Latin American Theoretical INformatics Symposium (LATIN 2018)
Abbreviated title	LATIN 2018
Country/Territory	Argentina
City	Buenos Aires
Period	16/04/18 → 19/04/18
Internet address	http://latin2018.dc.uba.ar/

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

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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. Bender, M. Farach-Colton, & M. A. Mosteiro (Eds.), LATIN 2018: Theoretical Informatics: 13th Latin American Symposium, Buenos Aires, Argentina, April 16-19, 2018, 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. 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, Buenos Aires, Argentina, April 16-19, 2018, Proceedings. editor / M.A. Bender ; M. Farach-Colton ; M.A. Mosteiro. Dordrecht : Springer, 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.",

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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 Bender, M Farach-Colton & MA Mosteiro (eds), LATIN 2018: Theoretical Informatics: 13th Latin American Symposium, Buenos Aires, Argentina, April 16-19, 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10807 LNCS, Springer, Dordrecht, pp. 187-200, 13th Latin American Theoretical INformatics Symposium (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, Buenos Aires, Argentina, April 16-19, 2018, Proceedings. ed. / M.A. Bender; M. Farach-Colton; M.A. Mosteiro. Dordrecht: Springer, 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 › Academic › peer-review

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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 Bender MA, Farach-Colton M, Mosteiro MA, editors, LATIN 2018: Theoretical Informatics: 13th Latin American Symposium, Buenos Aires, Argentina, April 16-19, 2018, Proceedings. Dordrecht: Springer. 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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