Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Matroids in Parameterized Complexity and Exact Algorithms

  • Fahad PanolanEmail author
  • Saket Saurabh
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_783

Years and Authors of Summarized Original Work

  • 2009; Marx

  • 2014; Fomin, Lokshtanov, Saurabh

  • 2014; Fomin, Lokshtanov, Panolan, Saurabh

  • 2014; Shachnai, Zehavi

Problem Definition

In recent years matroids have been used in the fields of parameterized complexity and exact algorithms. Many of these works mainly use a computation of representative families. Let \(M = (E,\mathcal{I})\)

Keywords

Exact algorithms Matroids Parameterized algorithms Representative families 
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Bollobás B (1965) On generalized graphs. Acta Math Acad Sci Hungar 16:447–452MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Fomin FV, Lokshtanov D, Panolan F, Saurabh S (2014) Representative sets of product families. In: Proceedings of 22nd Annual European Symposium on Algorithms (ESA 2014), Wroclaw, 8–10 Sept 2014, vol 8737, pp 443–454. DOI:10.1007/978-3-662-44777-2_37Google Scholar
  3. 3.
    Fomin FV, Lokshtanov D, Saurabh S (2014) Efficient computation of representative sets with applications in parameterized and exact algorithms. In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2014), Portland, 5–7 Jan 2014, pp 142–151. DOI:10.1137/1.9781611973402.10Google Scholar
  4. 4.
    Lokshtanov D, Misra P, Panolan F, Saurabh S (2015) Deterministic truncation of linear matroids. In: Proceedings of 42nd International Colloquium on Automata, Languages, and Programming (ICALP 2015), Kyoto, 6–10 July 2015, Part I, pp 922–934. DOI:10.1007/978-3-662-47672-7_75Google Scholar
  5. 5.
    Lovász L (1977) Flats in matroids and geometric graphs. In: Combinatorial surveys (Proceedings of the Sixth British Combinatorial Conference, Royal Holloway College, Egham). Academic, London, pp 45–86Google Scholar
  6. 6.
    Marx D (2006) Parameterized coloring problems on chordal graphs. Theor Comput Sci 351(3):407–424MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Marx D (2009) A parameterized view on matroid optimization problems. Theor Comput Sci 410(44):4471–4479MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Monien B (1985) How to find long paths efficiently. In: Analysis and design of algorithms for combinatorial problems (Udine, 1982). North-Holland mathematics studies, vol 109. North-Holland, Amsterdam, pp 239–254. DOI:10.1016/S0304-0208(08)73110-4Google Scholar
  9. 9.
    Shachnai H, Zehavi M (2014) Representative families: a unified tradeoff-based approach. In: Proceedings of 22nd Annual European Symposium on Algorithms (ESA 2014), Wroclaw, 8–10 Sept 2014, vol 8737, pp 786–797. DOI:10.1007/978-3-662-44777-2_65Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Mathematical SciencesChennaiIndia
  2. 2.Institute of Mathematical SciencesChennaiIndia
  3. 3.University of BergenBergenNorway