Fixed-Parameter Tractability, A Prehistory,

  • Michael A. Langston
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7370)


Many of the foundational parameterized tenets discussed in this festschrift actually predate by over a decade the first systematic treatments of fixed-parameter tractability. In this frank, firsthand account I will, to the best of my recollection, describe some of the earliest research avenues Mike Fellows and I pursued that would turn out later to be highly relevant to parameterized complexity. Although we did not know it at the time, these were the origins and formative years of this burgeoning new field. Readers unfamiliar with the history of fixed-parameter tractability may be surprised to learn that its initial motivations arose from, of all things, automation and optimization for integrated circuit design.


Planar Graph Vertex Cover Layout Problem Very Large Scale Integration Theoretical Computer Science 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chen, J., Kanj, I.A., Xia, G.: Simplicity is beauty: Improved upper bounds for vertex cover. Technical Report TR05-008, DePaul University, Chicago, Illinois (2005)Google Scholar
  2. 2.
    Deo, N., Krishnamoorthy, M.S., Langston, M.A.: Exact and approximate solutions for the gate matrix layout problem. IEEE Transactions on Computer Aided Design 6, 79–84 (1987)CrossRefGoogle Scholar
  3. 3.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
  4. 4.
    Fellows, M.R., Langston, M.A.: Nonconstructive advances in polynomial-time complexity. Information Processing Letters 26, 157–162 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fellows, M.R., Langston, M.A.: Nonconstructive tools for proving polynomial-time decidability. Journal of the ACM 35, 727–739 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fellows, M.R., Langston, M.A.: On search, decision and the efficiency of polynomial-time algorithms. In: Proceedings of ACM Symposium on Theory of Computing, pp. 501–512 (1989)Google Scholar
  7. 7.
    Fellows, M.R., Langston, M.A.: On well-partial-order theory and its application to combinatorial problems of VLSI design. SIAM Journal on Discrete Mathematics 5, 117–126 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of \(\cal NP\)-Completeness. W.H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  9. 9.
    Kashiwabara, T., Fujisawa, T.: An \(\cal NP\)-complete problem on interval graphs. In: Proceedings of IEEE Symposium on Circuits and Systems, pp. 657–660 (1979)Google Scholar
  10. 10.
    Kinnersley, N.G.: The vertex separation of a graph equals its path-width. Information Processing Letters 42, 345–350 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kinnersley, N.G., Langston, M.A.: Obstruction set isolation for the gate matrix layout problem. Discrete Applied Mathematics 54, 169–213 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kuratowski, K.: Sur le problème des courbes gaushes en topologie. Fundamenta Mathematicae (French) 15, 271–283 (1930)zbMATHGoogle Scholar
  13. 13.
    Levin, L.A.: Universal enumeration problems. Problemic Peredaci Informacii (Russian) 3, 115–116 (1972)Google Scholar
  14. 14.
    Lopez, A.D., Law, H.-F.S.: A dense gate matrix layout method for MOS VLSI. IEEE Transactions on Electron Devices 27, 1671–1675 (1980)CrossRefGoogle Scholar
  15. 15.
    Robertson, N., Seymour, P.D.: Disjoint paths - a survey. Journal of Algebraic and Discrete Methods 6, 300–305 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Robertson, N., Seymour, P.D.: Graph minors IV. Tree-width and well-quasi-ordering. Journal of Combinatorial Theory, Series B 48, 227–254 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Robertson, N., Seymour, P.D.: Graph minors XIII. The disjoint paths problem. Journal of Combinatorial Theory, Series B 63, 65–110 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Robertson, N., Seymour, P.D.: Graph minors XX. Wagner’s conjecture. Journal of Combinatorial Theory, Series B 92, 325–357 (2004)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michael A. Langston
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of TennesseeKnoxvilleUSA

Personalised recommendations