Document Open Access Logo

An FPT Algorithm for Elimination Distance to Bounded Degree Graphs

Authors Akanksha Agrawal , Lawqueen Kanesh , Fahad Panolan , M. S. Ramanujan , Saket Saurabh

PDF

File

Thumbnail PDF
PDF
LIPIcs.STACS.2021.5.pdf
  • Filesize: 0.74 MB
  • 11 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Elimination Distance
  • Fixed-parameter Tractability
  • Graph Modification

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

In the literature on parameterized graph problems, there has been an increased effort in recent years aimed at exploring novel notions of graph edit-distance that are more powerful than the size of a modulator to a specific graph class. In this line of research, Bulian and Dawar [Algorithmica, 2016] introduced the notion of elimination distance and showed that deciding whether a given graph has elimination distance at most k to any minor-closed class of graphs is fixed-parameter tractable parameterized by k [Algorithmica, 2017]. They showed that Graph Isomorphism parameterized by the elimination distance to bounded degree graphs is fixed-parameter tractable and asked whether determining the elimination distance to the class of bounded degree graphs is fixed-parameter tractable. Recently, Lindermayr et al. [MFCS 2020] obtained a fixed-parameter algorithm for this problem in the special case where the input is restricted to K₅-minor free graphs. 
In this paper, we answer the question of Bulian and Dawar in the affirmative for general graphs. In fact, we give a more general result capturing elimination distance to any graph class characterized by a finite set of graphs as forbidden induced subgraphs.

Cite As Get BibTex

Akanksha Agrawal, Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, and Saket Saurabh. An FPT Algorithm for Elimination Distance to Bounded Degree Graphs. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 5:1-5:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.STACS.2021.5

Author Details

Akanksha Agrawal
  • Indian Institute of Technology Madras, Chennai, India
Lawqueen Kanesh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
Fahad Panolan
  • Indian Institute of Technology, Hyderabad, India
M. S. Ramanujan
  • University of Warwick, Coventry, UK
Saket Saurabh
  • University of Bergen, Norway
  • The Institute of Mathematical Sciences, HBNI, Chennai, India

Funding

  • Agrawal, Akanksha: Supported by New Faculty Initiative Grant, IIT Madras, Chennai, India.
  • Panolan, Fahad: Supported by Seed grant, IIT Hyderabad (SG/IITH/F224/2020-21/SG-79).
  • Ramanujan, M. S.: Supported by EPSRC grant EP/V007793/1.
  • Saurabh, Saket: Supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819416) and Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18.

References

  1. Stefan Arnborg, Jens Lagergren, and Detlef Seese. Easy problems for tree-decomposable graphs. Journal of Algorithms, 12:308-340, 1991. Google Scholar
  2. Hans L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996. URL: https://doi.org/10.1137/S0097539793251219.
  3. Marin Bougeret, Bart M. P. Jansen, and Ignasi Sau. Bridge-depth characterizes which structural parameterizations of vertex cover admit a polynomial kernel. In Artur Czumaj, Anuj Dawar, and Emanuela Merelli, editors, 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 16:1-16:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ICALP.2020.16.
  4. Adam Bouland, Anuj Dawar, and Eryk Kopczynski. On tractable parameterizations of graph isomorphism. In Dimitrios M. Thilikos and Gerhard J. Woeginger, editors, Parameterized and Exact Computation - 7th International Symposium, IPEC 2012, Ljubljana, Slovenia, September 12-14, 2012. Proceedings, volume 7535 of Lecture Notes in Computer Science, pages 218-230. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-33293-7_21.
  5. Jannis Bulian and Anuj Dawar. Graph isomorphism parameterized by elimination distance to bounded degree. Algorithmica, 75(2):363-382, 2016. URL: https://doi.org/10.1007/s00453-015-0045-3.
  6. Jannis Bulian and Anuj Dawar. Fixed-parameter tractable distances to sparse graph classes. Algorithmica, 79(1):139-158, 2017. URL: https://doi.org/10.1007/s00453-016-0235-7.
  7. Rajesh Chitnis, Marek Cygan, MohammadTaghi Hajiaghayi, Marcin Pilipczuk, and Michal Pilipczuk. Designing FPT algorithms for cut problems using randomized contractions. SIAM J. Comput., 45(4):1171-1229, 2016. URL: https://doi.org/10.1137/15M1032077.
  8. Bruno Courcelle. The monadic second-order logic of graphs I: Recognizable sets of finite graphs. Inform. and Comput., 85:12-75, 1990. Google Scholar
  9. Bruno Courcelle. The expression of graph properties and graph transformations in monadic second-order logic. In Handbook of graph grammars and computing by graph transformation, Vol. 1, pages 313-400. World Sci. Publ, River Edge, NJ, 1997. Google Scholar
  10. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21275-3.
  11. Eduard Eiben, Robert Ganian, Thekla Hamm, and O-joung Kwon. Measuring what matters: A hybrid approach to dynamic programming with treewidth. In Peter Rossmanith, Pinar Heggernes, and Joost-Pieter Katoen, editors, 44th International Symposium on Mathematical Foundations of Computer Science, MFCS 2019, August 26-30, 2019, Aachen, Germany, volume 138 of LIPIcs, pages 42:1-42:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.MFCS.2019.42.
  12. Eduard Eiben, Robert Ganian, and Stefan Szeider. Meta-kernelization using well-structured modulators. In Thore Husfeldt and Iyad A. Kanj, editors, 10th International Symposium on Parameterized and Exact Computation, IPEC 2015, September 16-18, 2015, Patras, Greece, volume 43 of LIPIcs, pages 114-126. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. URL: https://doi.org/10.4230/LIPIcs.IPEC.2015.114.
  13. Fedor V. Fomin and Yngve Villanger. Treewidth computation and extremal combinatorics. Comb., 32(3):289-308, 2012. URL: https://doi.org/10.1007/s00493-012-2536-z.
  14. Robert Ganian, Sebastian Ordyniak, and M. S. Ramanujan. Going beyond primal treewidth for (M)ILP. In Satinder P. Singh and Shaul Markovitch, editors, Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, February 4-9, 2017, San Francisco, California, USA, pages 815-821. AAAI Press, 2017. URL: http://aaai.org/ocs/index.php/AAAI/AAAI17/paper/view/14272.
  15. Robert Ganian, M. S. Ramanujan, and Stefan Szeider. Combining treewidth and backdoors for CSP. In Heribert Vollmer and Brigitte Vallée, editors, 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017, March 8-11, 2017, Hannover, Germany, volume 66 of LIPIcs, pages 36:1-36:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.STACS.2017.36.
  16. Jiong Guo, Falk Hüffner, and Rolf Niedermeier. A structural view on parameterizing problems: Distance from triviality. In Rodney G. Downey, Michael R. Fellows, and Frank K. H. A. Dehne, editors, Parameterized and Exact Computation, First International Workshop, IWPEC 2004, Bergen, Norway, September 14-17, 2004, Proceedings, volume 3162 of Lecture Notes in Computer Science, pages 162-173. Springer, 2004. URL: https://doi.org/10.1007/978-3-540-28639-4_15.
  17. Eva-Maria C. Hols, Stefan Kratsch, and Astrid Pieterse. Elimination distances, blocking sets, and kernels for vertex cover. In Christophe Paul and Markus Bläser, editors, 37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020, March 10-13, 2020, Montpellier, France, volume 154 of LIPIcs, pages 36:1-36:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.STACS.2020.36.
  18. Alexander Lindermayr, Sebastian Siebertz, and Alexandre Vigny. Elimination distance to bounded degree on planar graphs. In Javier Esparza and Daniel Král', editors, 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, August 24-28, 2020, Prague, Czech Republic, volume 170 of LIPIcs, pages 65:1-65:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.MFCS.2020.65.
  19. Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh, and Meirav Zehavi. Reducing CMSO model checking to highly connected graphs. In Ioannis Chatzigiannakis, Christos Kaklamanis, Dániel Marx, and Donald Sannella, editors, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, July 9-13, 2018, Prague, Czech Republic, volume 107 of LIPIcs, pages 135:1-135:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.ICALP.2018.135.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact