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The Parameterized Complexity of Dominating Set and Friends Revisited for Structured Graphs

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Computer Science – Theory and Applications (CSR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11532))

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Abstract

We consider variants and generalizations of the dominating set problem on special classes of graphs, specifically, graphs that are a small distance from a tractable class. Here, our focus is mainly on the problems of domination and efficient domination (a variant where we want every vertex to be dominated uniquely) and their respective generalizations to -distance domination.

We consider graphs which are at most vertices away from the following classes: edgless graphs, cluster graphs, split graphs, and complements of bipartite graphs. For the newly introduced parameter CBDS, we show that Dominating Set is W[2]-hard , while in contrast, is FPT for . For this parameter, Efficient Dominating Set turns out to be FPT as well. We generalize known results for Dominating Set parameterized by CVD to parameterized by CVD, inspired by algorithms for parameterized by VC, which is in general a larger parameter. We are also able to do this for the Efficient Dominating Set problem. Finally, for the problem of efficient domination parameterized by the distance to split graphs, we improve the complexity of the known algorithm from to .

For the most part, our results generalize what is known in the current landscape, both in terms of obtaining algorithms for smaller parameters, as well as for the more general notion of domination itself, which is to dominate over larger distances.

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References

  1. Borradaile, G., Le, H.: Optimal dynamic program for r-domination problems over tree decompositions. In: 11th International Symposium on Parameterized and Exact Computation, IPEC 2016, August 24–26, 2016, Aarhus, Denmark, pp. 8:1–8:23 (2016)

    Google Scholar 

  2. Cygan, M., et al.: Parameterized Algorithms. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21275-3

    Book  MATH  Google Scholar 

  3. Goyal, D., Jacob, A., Kumar, K., Majumdar, D., Raman, V.: Structural parameterizations of dominating set variants. In: Fomin, F.V., Podolskii, V.V. (eds.) CSR 2018. LNCS, vol. 10846, pp. 157–168. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-90530-3_14

    Chapter  Google Scholar 

  4. Katsikarelis, I., Lampis, M., Paschos, V.Th.: Structural parameters, tight bounds, and approximation for (k, r)-center. In: Proceedings of the 28th International Symposium on Algorithms and Computation, ISAAC, pp. 50:1–50:13 (2017)

    Google Scholar 

  5. Misra, N., Philip, G., Raman, V., Saurabh, S.: The effect of girth on the kernelization complexity of connected dominating set. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, December 15–18, 2010, Chennai, India, pp. 96–107 (2010)

    Google Scholar 

  6. Philip, G., Raman, V., Sikdar, S.: Solving dominating set in larger classes of graphs: FPT algorithms and polynomial kernels. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 694–705. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04128-0_62

    Chapter  MATH  Google Scholar 

  7. Raman, V., Saurabh, S.: Short cycles make W-hard problems hard: FPT algorithms for W-hard problems in graphs with no short cycles. Algorithmica 52(2), 203–225 (2008)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors thank the reviewers for their detailed comments which have helped improve the presentation of the manuscript. This work is supported by the SERB project MTR/2017/001033.

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Authors and Affiliations

  1. Indian Institute of Technology, Gandhinagar, Palaj, Gandhinagar, 382355, India

    Neeldhara Misra & Piyush Rathi

Authors
  1. Neeldhara Misra
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  2. Piyush Rathi
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Correspondence to Neeldhara Misra .

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Editors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    René van Bevern

  2. Laboratoire d'Informatique Gaspard-Monge, Marne-la-Vallée, France

    Gregory Kucherov

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Misra, N., Rathi, P. (2019). The Parameterized Complexity of Dominating Set and Friends Revisited for Structured Graphs. In: van Bevern, R., Kucherov, G. (eds) Computer Science – Theory and Applications. CSR 2019. Lecture Notes in Computer Science(), vol 11532. Springer, Cham. https://doi.org/10.1007/978-3-030-19955-5_26

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  • DOI: https://doi.org/10.1007/978-3-030-19955-5_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19954-8

  • Online ISBN: 978-3-030-19955-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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