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Splitting \(B_2\)-VPG Graphs into Outer-String and Co-Comparability Graphs

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Algorithms and Data Structures (WADS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10389))

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Abstract

A \(B_2\)-VPG representation of a graph is an intersection representation that consists of orthogonal curves with at most 2 bends. In this paper, we show that the curves of such a representation can be partitioned into \(O(\log n)\) groups that represent outer-string graphs or \(O(\log ^3 n)\) groups that represent permutation graphs. This leads to better approximation algorithms for hereditary graph problems, such as independent set, clique and clique cover, on \(B_2\)-VPG graphs.

T.B. was supported by NSERC; M.D. was supported by Vanier CGS.

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Therese Biedl & Martin Derka

Authors
  1. Therese Biedl
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  2. Martin Derka
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Correspondence to Martin Derka .

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Editors and Affiliations

  1. Computer Science, University of Toronto , Toronto, Ontario, Canada

    Faith Ellen

  2. Computer Science, Memorial University of Newfoundland , St. John’s, Newfoundland and Labrador, Canada

    Antonina Kolokolova

  3. Carleton University, Ottawa, Ontario, Canada

    Jörg-Rüdiger Sack

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Biedl, T., Derka, M. (2017). Splitting \(B_2\)-VPG Graphs into Outer-String and Co-Comparability Graphs. In: Ellen, F., Kolokolova, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2017. Lecture Notes in Computer Science(), vol 10389. Springer, Cham. https://doi.org/10.1007/978-3-319-62127-2_14

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  • DOI: https://doi.org/10.1007/978-3-319-62127-2_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62126-5

  • Online ISBN: 978-3-319-62127-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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