Skip to main content
SpringerLink
Log in

Bidimensionality

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 2004; Demaine, Fomin, Hajiaghayi; Thilikos

  • 2004; Demaine, Hajiaghayi

  • 2005; Demaine, Fomin, Hajiaghayi, Thilikos

  • 2005; Demaine, Hajiaghayi

  • 2006; Demaine, Hajiaghayi, Thilikos

  • 2008; Demaine, Hajiaghayi

  • 2008; Dorn, Fomin, Thilikos

  • 2009; Fomin, Golovach, Thilikos

  • 2010; Demaine

  • 2010; Fomin, Lokshtanov, Saurabh, Thilikos

  • 2011; Fomin, Lokshtanov, Raman, Saurabh

  • 2011; Fomin, Golovach, Thilikos

  • 2012; Fomin, Lokshtanov, Saurabh

  • 2013; Giannopoulou, Thilikos

  • 2013; Demaine, Fomin, Hajiaghayi, Thilikos

  • 2014; Grigoriev, Koutsonas, Thilikos

Problem Definition

The theory of bidimensionality provides general techniques for designing efficient fixed-parameter algorithms and approximation algorithms for a broad range of NP-hard graph problems in a broad range of graphs. This theory applies to graph problems that are “bidimensional” in the sense that (1) the solution value for the k × k grid graph and similar graphs grows with k, typically as \(\varOmega...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,999.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

  1. Demaine ED, Fomin FV, Hajiaghayi M, Thilikos DM (2004) Bidimensional parameters and local treewidth. SIAM J Discret Math 18(3):501–511

    Article  MathSciNet  MATH  Google Scholar 

  2. Demaine ED, Fomin FV, Hajiaghayi M, Thilikos DM (2005) Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs. ACM Trans Algorithms 1(1):33–47

    Google Scholar 

  3. Demaine ED, Fomin FV, Hajiaghayi M, Thilikos DM (2005) Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs. J ACM 52(6):866–893

    Article  MathSciNet  MATH  Google Scholar 

  4. Demaine ED, Hajiaghayi M (to appear) The bidimensionality theory and its algorithmic applications. Comput J

    Google Scholar 

  5. Demaine ED, Hajiaghayi M (2004) Diameter and treewidth in minor-closed graph families, revisited. Algorithmica 40(3):211–215

    Article  MathSciNet  MATH  Google Scholar 

  6. Demaine ED, Hajiaghayi M (2004) Equivalence of local treewidth and linear local treewidth and its algorithmic applications. In: Proceedings of the 15th ACM-SIAM symposium on discrete algorithms (SODA’04), New Orleans, Jan 2004, pp 833–842

    Google Scholar 

  7. Demaine ED, Hajiaghayi M (2005) Bidimensionality: new connections between FPT algorithms and PTASs. In: Proceedings of the 16th annual ACM-SIAM symposium on discrete algorithms (SODA 2005), Vancouver, Jan 2005, pp 590–601

    Google Scholar 

  8. Demaine ED, Hajiaghayi M (2005) Graphs excluding a fixed minor have grids as large as treewidth, with combinatorial and algorithmic applications through bidimensionality. In: Proceedings of the 16th annual ACM-SIAM symposium on discrete algorithms (SODA 2005), Vancouver, Jan 2005, pp 682–689

    Google Scholar 

  9. Demaine ED, Hajiaghayi M, Kawarabayashi K (2006) Algorithmic graph minor theory: improved grid minor bounds and Wagner’s contraction. In: Proceedings of the 17th annual international symposium on algorithms and computation, Calcutta, Dec 2006. Lecture notes in computer science, vol 4288, pp 3–15

    Google Scholar 

  10. Demaine ED, Hajiaghayi M, Nishimura N, Ragde P, Thilikos DM (2004) Approximation algorithms for classes of graphs excluding single-crossing graphs as minors. J Comput Syst Sci 69(2):166–195

    Article  MathSciNet  MATH  Google Scholar 

  11. Demaine ED, Hajiaghayi M, Thilikos DM (2005) Exponential speedup of fixed-parameter algorithms for classes of graphs excluding single-crossing graphs as minors. Algorithmica 41(4):245–267

    Article  MathSciNet  MATH  Google Scholar 

  12. Demaine ED, Hajiaghayi M, Thilikos DM (2006) The bidimensional theory of bounded-genus graphs. SIAM J Discret Math 20(2):357–371

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Fedor V. Fomin

  2. MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA, USA

    Erik D. Demaine

  3. Department of Computer Science, University of Maryland, College Park, MD, USA

    Mohammad Taghi Hajiaghayi

  4. AlGCo Project-Team, CNRS, LIRMM, Montpellier, France

    Dimitrios Thilikos

  5. Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece

    Dimitrios Thilikos

Authors
  1. Fedor V. Fomin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik D. Demaine
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Taghi Hajiaghayi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dimitrios Thilikos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fedor V. Fomin .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this entry

Cite this entry

Fomin, F.V., Demaine, E.D., Hajiaghayi, M.T., Thilikos, D. (2016). Bidimensionality. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_47

Download citation

Publish with us

Policies and ethics

Search

Navigation