On approximate preprocessing for domination and hitting subgraphs with connected deletion sets

Eduard Eiben; Danny Hermelin; M. S. Ramanujan

doi:10.1016/j.jcss.2019.05.001

On approximate preprocessing for domination and hitting subgraphs with connected deletion sets

Eduard Eiben, Danny Hermelin, M. S. Ramanujan

Department of Industrial Engineering and Management

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the CONNECTED H-HITTING SET and DOMINATING SET problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the CONNECTED H-HITTING SET problem, we obtain an α-approximate kernel for every α>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the DOMINATING SET problem on d-degenerate graphs, and provide an interpolation of approximate kernels between the known 3d-approximate kernel of constant size and 1-approximate kernel of size k^O(d²).

Original language	American English
Pages (from-to)	158-170
Number of pages	13
Journal	Journal of Computer and System Sciences
Volume	105
DOIs	https://doi.org/10.1016/j.jcss.2019.05.001
State	Published - 1 Nov 2019

Keywords

Kernelization
Parameterized complexity
Vertex deletion problems

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science
Applied Mathematics
Computer Networks and Communications
Computational Theory and Mathematics

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10.1016/j.jcss.2019.05.001

Cite this

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abstract = "In this paper, we study the CONNECTED H-HITTING SET and DOMINATING SET problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the CONNECTED H-HITTING SET problem, we obtain an α-approximate kernel for every α>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the DOMINATING SET problem on d-degenerate graphs, and provide an interpolation of approximate kernels between the known 3d-approximate kernel of constant size and 1-approximate kernel of size kO(d2).",

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AU - Hermelin, Danny

AU - Ramanujan, M. S.

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N2 - In this paper, we study the CONNECTED H-HITTING SET and DOMINATING SET problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the CONNECTED H-HITTING SET problem, we obtain an α-approximate kernel for every α>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the DOMINATING SET problem on d-degenerate graphs, and provide an interpolation of approximate kernels between the known 3d-approximate kernel of constant size and 1-approximate kernel of size kO(d2).

AB - In this paper, we study the CONNECTED H-HITTING SET and DOMINATING SET problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the CONNECTED H-HITTING SET problem, we obtain an α-approximate kernel for every α>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the DOMINATING SET problem on d-degenerate graphs, and provide an interpolation of approximate kernels between the known 3d-approximate kernel of constant size and 1-approximate kernel of size kO(d2).

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KW - Parameterized complexity

KW - Vertex deletion problems

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JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

ER -

On approximate preprocessing for domination and hitting subgraphs with connected deletion sets

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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