Document Open Access Logo

Typical Sequences Revisited - Computing Width Parameters of Graphs

Authors Hans L. Bodlaender , Lars Jaffke , Jan Arne Telle

PDF
Thumbnail PDF

File

LIPIcs.STACS.2020.57.pdf
  • Filesize: 0.95 MB
  • 16 pages

Document Identifiers

Author Details

Hans L. Bodlaender
  • Department of Computer Science, Utrecht University, The Netherlands
Lars Jaffke
  • Department of Informatics, University of Bergen, Norway
Jan Arne Telle
  • Department of Informatics, University of Bergen, Norway

Funding

  • Bodlaender, Hans L.: Partially supported by the Networks project, funded by the Netherlands Organization for Scientific Research (NWO).
  • Jaffke, Lars: Supported by the Bergen Research Foundation (BFS).

Acknowledgements

This work was started when the third author was visiting Universitat Politecnica de Valencia, and part of it was done while the second author was visiting Utrecht University.

Cite As Get BibTex

Hans L. Bodlaender, Lars Jaffke, and Jan Arne Telle. Typical Sequences Revisited - Computing Width Parameters of Graphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.STACS.2020.57

Abstract

In this work, we give a structural lemma on merges of typical sequences, a notion that was introduced in 1991 [Lagergren and Arnborg, Bodlaender and Kloks, both ICALP 1991] to obtain constructive linear time parameterized algorithms for treewidth and pathwidth. The lemma addresses a runtime bottleneck in those algorithms but so far it does not lead to asymptotically faster algorithms. However, we apply the lemma to show that the cutwidth and the modified cutwidth of series parallel digraphs can be computed in ?(n²) time.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • typical sequences
  • treewidth
  • series parallel digraphs
  • cutwidth
  • modified cutwidth

Metrics

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

Related Versions

References

  1. Ernst Althaus and Sarah Ziegler. Optimal tree decompositions revisited: A simpler linear-time FPT algorithm, 2019. URL: http://arxiv.org/abs/1912.09144.
  2. Eyal Amir. Approximation algorithms for treewidth. Algorithmica, 56(4):448-479, 2010. Google Scholar
  3. Hans L. Bodlaender. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput., 25(6):1305-1317, 1996. Google Scholar
  4. Hans L. Bodlaender, Leizhen Cai, Jianer Chen, Michael R. Fellows, Jan Arne Telle, and Dániel Marx. Open problems in parameterized and exact computation - IWPEC 2006. Technical Report UU-CS-2006-052, Department of Information and Computing Sciences, Utrecht University, 2006. Google Scholar
  5. Hans L. Bodlaender, Pål Grønås Drange, Markus S. Dregi, Fedor V. Fomin, Daniel Lokshtanov, and Michał Pilipczuk. A c^kn 5-approximation algorithm for treewidth. SIAM J. Comput., 45(2):317-378, 2016. Google Scholar
  6. Hans L. Bodlaender, Michael R. Fellows, and Dimitrios M. Thilikos. Derivation of algorithms for cutwidth and related graph layout parameters. J. Comput. Syst. Sci., 75(4):231-244, 2009. Google Scholar
  7. Hans L. Bodlaender, Jens Gustedt, and Jan Arne Telle. Linear-time register allocation for a fixed number of registers. In Proc. 9th SODA, pages 574-583. ACM/SIAM, 1998. Google Scholar
  8. Hans L. Bodlaender and Ton Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. J. Algorithms, 21(2):358-402, 1996. Google Scholar
  9. Hans L. Bodlaender and Dimitrios M. Thilikos. Constructive linear time algorithms for branchwidth. In Proc. 24th ICALP, volume 1256 of LNCS, pages 627-637. Springer, 1997. Google Scholar
  10. Hans L. Bodlaender and Dimitrios M. Thilikos. Computing small search numbers in linear time. In Proc. 1st IWPEC, volume 3162 of LNCS, pages 37-48. Springer, 2004. Google Scholar
  11. Mikolaj Bojanczyk and Michal Pilipczuk. Optimizing tree decompositions in MSO. In Proc. 34th STACS, volume 66 of LIPIcs, pages 15:1-15:13, 2017. Google Scholar
  12. Uriel Feige, MohammadTaghi Hajiaghayi, and James R. Lee. Improved approximation algorithms for minimum weight vertex separators. SIAM J. Comput., 38(2):629-657, 2008. Google Scholar
  13. Martin Fürer. Faster computation of path-width. In Proc. 27th IWOCA, volume 9843 of LNCS, pages 385-396. Springer, 2016. Google Scholar
  14. Jens Lagergren. Efficient parallel algorithms for graphs of bounded tree-width. J. Algorithms, 20(1):20-44, 1996. Google Scholar
  15. Jens Lagergren and Stefan Arnborg. Finding minimal forbidden minors using a finite congruence. In Proc. 18th ICALP, volume 510 of LNCS, pages 532-543. Springer, 1991. Google Scholar
  16. Bruce A. Reed. Finding approximate separators and computing tree width quickly. In Proc. 24th STOC, pages 221-228. ACM, 1992. Google Scholar
  17. Neil Robertson and Paul D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory, Ser. B, 63(1):65-110, 1995. Google Scholar
  18. Dimitrios M. Thilikos, Maria J. Serna, and Hans L. Bodlaender. Cutwidth I: A linear time fixed parameter algorithm. J. Algorithms, 56(1):1-24, 2005. Google Scholar
  19. Dimitrios M. Thilikos, Maria J. Serna, and Hans L. Bodlaender. Cutwidth II: Algorithms for partial w-trees of bounded degree. J. Algorithms, 56(1):25-49, 2005. Google Scholar
  20. Jacobo Valdes, Robert E. Tarjan, and Eugene L. Lawler. The recognition of series-parallel digraphs. SIAM J. Comput., 11(2):298-313, 1982. Google Scholar
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
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact