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Linear MIM-Width of Trees

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Graph-Theoretic Concepts in Computer Science (WG 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11789))

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Abstract

We provide an \(O(n \log n)\) algorithm computing the linear maximum induced matching width of a tree and an optimal layout.

Long version with extra figures and full proofs is published on arxiv [12].

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References

  1. Adler, I., Kanté, M.M.: Linear rank-width and linear clique-width of trees. Theor. Comput. Sci. 589, 87–98 (2015)

    Article  MathSciNet  Google Scholar 

  2. Belmonte, R., Vatshelle, M.: Graph classes with structured neighborhoods and algorithmic applications. Theor. Comput. Sci. 511, 54–65 (2013)

    Article  MathSciNet  Google Scholar 

  3. Bergougnoux, B., Kanté, M.M.: Rank based approach on graphs with structured neighborhood. CoRR, abs/1805.11275 (2018)

    Google Scholar 

  4. Bui-Xuan, B.-M., Telle, J.A., Vatshelle, M.: Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems. Theor. Comput. Sci. 511, 66–76 (2013)

    Article  MathSciNet  Google Scholar 

  5. Diestel, R.: Graph Theory. Graduate Texts in Mathematics, vol. 173, 4th edn. Springer, Heidelberg (2012)

    MATH  Google Scholar 

  6. Ellis, J.A., Sudborough, I.H., Turner, J.S.: The vertex separation and search number of a graph. Inf. Comput. 113(1), 50–79 (1994)

    Article  MathSciNet  Google Scholar 

  7. Fomin, F.V., Golovach, P.A., Raymond, J.-F.: On the tractability of optimization problems on H-graphs. In: Proceedings of the ESA 2018, pp. 30:1–30:14 (2018)

    Google Scholar 

  8. Galby, E., Munaro, A., Ries, B.: Semitotal domination: new hardness results and a polynomial-time algorithm for graphs of bounded MIM-width. CoRR, abs/1810.06872 (2018)

    Google Scholar 

  9. Golovach, P.A., Heggernes, P., Kanté, M.M., Kratsch, D., Sæther, S.H., Villanger, Y.: Output-polynomial enumeration on graphs of bounded (local) linear MIM-width. Algorithmica 80(2), 714–741 (2018)

    Article  MathSciNet  Google Scholar 

  10. Golumbic, M.C., Rotics, U.: On the clique-width of some perfect graph classes. Int. J. Found. Comput. Sci. 11(3), 423–443 (2000)

    Article  MathSciNet  Google Scholar 

  11. Hlinený, P., Oum, S., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. Comput. J. 51(3), 326–362 (2008)

    Article  Google Scholar 

  12. Høgemo, S., Telle, J.A., Raa Vågset, E.: Linear MIM-width of trees. CoRR, arXiv:1907.04132 (2019)

  13. Jaffke, L., Kwon, O., Strømme, T.J.F., Telle, J.A.: Generalized distance domination problems and their complexity on graphs of bounded MIM-width. In 13th International Symposium on Parameterized and Exact Computation, IPEC 2018, Helsinki, Finland, 20–24 August 2018, pp. 6:1–6:14 (2018)

    Google Scholar 

  14. Jaffke, L., Kwon, O., Telle, J.A.: Polynomial-time algorithms for the longest induced path and induced disjoint paths problems on graphs of bounded MIM-width. In 12th International Symposium on Parameterized and Exact Computation, IPEC 2017, Vienna, Austria, 6–8 September 2017, pp. 21:1–21:13 (2017)

    Google Scholar 

  15. Jaffke, L., Kwon, O., Telle, J.A.: A unified polynomial-time algorithm for feedback vertex set on graphs of bounded MIM-width. In 35th Symposium on Theoretical Aspects of Computer Science, STACS 2018, Caen, France, 28 February–3 March 2018, pp. 42:1–42:14 (2018)

    Google Scholar 

  16. Mengel, S.: Lower bounds on the MIM-width of some graph classes. Discrete Appl. Math. 248, 28–32 (2018)

    Article  MathSciNet  Google Scholar 

  17. Möhring, R.H.: Graph problems related to gate matrix layout and PLA folding. In: Tinhofer, G., Mayr, E., Noltemeier, H., Syslo, M.M. (eds.) Computational Graph Theory. COMPUTING, vol. 7, pp. 17–51. Springer, Vienna (1990). https://doi.org/10.1007/978-3-7091-9076-0_2

    Chapter  Google Scholar 

  18. Oum, S.: Rank-width: algorithmic and structural results. Discrete Appl. Math. 231, 15–24 (2017)

    Article  MathSciNet  Google Scholar 

  19. Sæther, S.H., Vatshelle, M.: Hardness of computing width parameters based on branch decompositions over the vertex set. Theor. Comput. Sci. 615, 120–125 (2016)

    Article  MathSciNet  Google Scholar 

  20. Skodinis, K.: Construction of linear tree-layouts which are optimal with espect to vertex separation in linear time. J. Algorithms 47(1), 40–59 (2003)

    Article  MathSciNet  Google Scholar 

  21. Vatshelle, M.: New width parameters of graphs. Ph.D. thesis, University of Bergen, Norway (2012)

    Google Scholar 

  22. Yamazaki, K.: Inapproximability of rank, clique, Boolean, and maximum induced matching-widths under small set expansion hypothesis. Algorithms 11(11), 173 (2018)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Svein Høgemo, Jan Arne Telle & Erlend Raa Vågset

Authors
  1. Svein Høgemo
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  2. Jan Arne Telle
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  3. Erlend Raa Vågset
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Corresponding author

Correspondence to Svein Høgemo .

Editor information

Editors and Affiliations

  1. CNRS, LIRMM, Université de Montpellier, Montpellier, France

    Ignasi Sau

  2. CNRS, LIRMM, Université de Montpellier, Montpellier, France

    Dimitrios M. Thilikos

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Høgemo, S., Telle, J.A., Vågset, E.R. (2019). Linear MIM-Width of Trees. In: Sau, I., Thilikos, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2019. Lecture Notes in Computer Science(), vol 11789. Springer, Cham. https://doi.org/10.1007/978-3-030-30786-8_17

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  • DOI: https://doi.org/10.1007/978-3-030-30786-8_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30785-1

  • Online ISBN: 978-3-030-30786-8

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