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Computing Coverage Kernels Under Restricted Settings

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Computing and Combinatorics (COCOON 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10976))

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Abstract

We consider the Minimum Coverage Kernel problem: given a set \(\mathcal {B}\) of d-dimensional boxes, find a subset of \(\mathcal {B}\) of minimum size covering the same region as \(\mathcal {B}\). This problem is \(\mathsf {NP}\)-hard, but as for many \(\mathsf {NP}\)-hard problems on graphs, the problem becomes solvable in polynomial time under restrictions on the graph induced by \(\mathcal {B}\). We consider various classes of graphs, show that Minimum Coverage Kernel remains \(\mathsf {NP}\)-hard even for severely restricted instances, and provide two polynomial time approximation algorithms for this problem.

This work was supported by projects CONICYT Fondecyt/Regular nos 1170366 and 1160543, and CONICYT-PCHA/Doctorado Nacional/2013-63130209 (Chile).

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Notes

  1. 1.

    The incidence graph of a 3-SAT formula is a bipartite graph with a vertex for each variable and each clause, and an edge between a variable vertex and a clause vertex for each occurrence of a variable in a clause.

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Acknowledgments

We thank an anonymous reviewer for carefully reading our manuscript, and providing many insightful comments and suggestions.

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Authors and Affiliations

  1. Departamento de Ciencias de la Computación, Universidad de Chile, Santiago, Chile

    Jérémy Barbay & Javiel Rojas-Ledesma

  2. Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago, Santiago, Chile

    Pablo Pérez-Lantero

Authors
  1. Jérémy Barbay
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  2. Pablo Pérez-Lantero
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  3. Javiel Rojas-Ledesma
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Corresponding author

Correspondence to Jérémy Barbay .

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Editors and Affiliations

  1. City University of Hong Kong, Hong Kong, China

    Lusheng Wang

  2. Shandong University, Jinan, China

    Daming Zhu

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Barbay, J., Pérez-Lantero, P., Rojas-Ledesma, J. (2018). Computing Coverage Kernels Under Restricted Settings. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_16

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  • DOI: https://doi.org/10.1007/978-3-319-94776-1_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94775-4

  • Online ISBN: 978-3-319-94776-1

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