The Birth and Early Years of Parameterized Complexity

  • Rod Downey
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7370)


Through the hazy lens of (my) memory, I will try to reconstruct how Mike Fellows and I, together with some co-authors in some cases, came up with the basic papers in parameterized complexity.


Model Check Turing Machine Complexity Theory Parameterized Complexity Vertex Cover 
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. [ADF93]
    Abrahamson, K., Downey, R., Fellows, M.: Fixed Parameter Intractability II (Extended Abstract). In: Enjalbert, P., Wagner, K.W., Finkel, A. (eds.) STACS 1993. LNCS, vol. 665, pp. 374–385. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  2. [ADF95]
    Abrahamson, K., Downey, R., Fellows, M.: Fixed Parameter Tractability and Completeness IV: On Completeness for W[P] and PSPACE Analogs. Annals of Pure and Applied Logic 73, 235–276 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  3. [AEFM89]
    Abrahamson, K., Ellis, J., Fellows, M., Mata, M.: On the complexity of fixed-parameter problems. In: Proceedings of 13th FOCS, pp. 210–215 (1989)Google Scholar
  4. [AF93]
    Abrahamson, K., Fellows, M.: Finite Automata, Bounded Treewidth and Wellquasiordering. In: Graph Structure Theory. Contemporary Mathematics Series, vol. 147, pp. 539–564. American Mathematical Society (1993)Google Scholar
  5. [AR01]
    Alekhnovich, M., Razborov, A.: Resolution is Not Automatizable Unless W[P] is Tractable. In: Proc. of the 42nd IEEE FOCS, pp. 210–219 (2001)Google Scholar
  6. [AYZ94]
    Alon, N., Yuster, R., Zwick, U.: Color-Coding: A New Method for Finding Simple Paths, Cycles and Other Small Subgraphs Within Large Graphs. In: Proc. Symp. Theory of Computing (STOC), pp. 326–335. ACM (1994)Google Scholar
  7. [BDG87]
    Balcazaar, J., Diaz, J., Gabarro, J.: Structural Complexity, vol. 1. Springer (1987)Google Scholar
  8. [Baz95]
    Bazgan, C.: Schémas d’approximation et complexité paramétrée. Rapport de stage de DEA d’Informatique à Orsay (1995)Google Scholar
  9. [Bod93]
    Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. In: Proceedings of the 25th ACM Symposium on Theory of Computing, pp. 226–234 (1993)Google Scholar
  10. [Bod96]
    Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  11. [BDFH08]
    Bodlaender, H., Downey, R., Fellows, M., Hermelin, D.: On Problems without Polynomial Kernels (Extended Abstract). In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 563–574. Springer, Heidelberg (2008); Final version to appear in Journal of Computing and System SciencesCrossRefGoogle Scholar
  12. [BDFHW95]
    Bodlaender, H., Downey, R., Fellows, M., Hallett, M., Wareham, H.T.: Parameterized Complexity Analysis in Computational Biology. Computer Applications in the Biosciences 11, 49–57 (1995)Google Scholar
  13. [BDFW95]
    Bodlaender, H., Downey, R., Fellows, M., Wareham, H.T.: The Parameterized Complexity of the Longest Common Subsequence Problem. Theoretical Computer Science A 147, 31–54 (1995)CrossRefzbMATHGoogle Scholar
  14. [BF95]
    Bodlaender, H., Fellows, M.: On the Complexity of k-Processor Scheduling. Operations Research Letters 18, 93–98 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [BFH94]
    Bodlaender, H., Fellows, M.R., Hallett, M.T.: Beyond NP-completeness for Problems of Bounded Width: Hardness for the W Hierarchy. In: Proc. ACM Symp. on Theory of Computing (STOC), pp. 449–458 (1994)Google Scholar
  16. [La75]
    Ladner, R.: On the Structure of Polynomial Tine Reducibility. Journal of the Association for Computing Machinery 22, 155–171 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  17. [LeC96]
    Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters 58(4), 171–176 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  18. [CC97]
    Cai, L., Chen, J.: On Fixed-Parameter Tractability and Approximability of NP-Hard Optimization Problems. J. Computer and Systems Sciences 54, 465–474 (1997)CrossRefzbMATHGoogle Scholar
  19. [CCDF96]
    Cai, L., Chen, J., Downey, R.G., Fellows, M.R.: On the Parameterized Complexity of Short Computation and Factorization. Arch. for Math. Logic 36, 321–337 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  20. [CCDF97]
    Cai, L., Chen, J., Downey, R., Fellows, M.: Advice Classes of Parameterized Tractability. Annals of Pure and Applied Logic 84, 119–138 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  21. [Co87]
    Courcelle, B.: Recognizability and Second-Order Definability for Sets of Finite Graphs. Technical Report I-8634, Universite de Bordeaux (1987)Google Scholar
  22. [CDF97]
    Courcelle, B., Downey, R., Fellows, M.: A Note on the Computability of Graph Minor Obstruction Sets for Monadic Second Order Ideals. Journal of Universal Computer Science 3, 1194–1198 (1997)MathSciNetzbMATHGoogle Scholar
  23. [CW95]
    Cesati, M., Wareham, H.T.: Parameterized Complexity Analysis in Robot Motion Planning. In: Proceedings 25th IEEE Intl. Conf. on Systems, Man and Cybernetics, vol. 1, pp. 880–885. IEEE Press, Los Alamitos (1995)Google Scholar
  24. [Do12]
    Downey, R.: A Basic Parameterized Complexity Primer. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 91–128. Springer, Heidelberg (2012)Google Scholar
  25. [DEF93]
    Downey, R., Evans, P., Fellows, M.: Parameterized Learning Complexity. In: Proc. 6th ACM Workshop on Computational Learning Theory, pp. 51–57 (1993)Google Scholar
  26. [DF91]
    Downey, R., Fellows, M.: A completeness theory for fixed parameter problems, March 25 (1991) (unpublished manuscript)Google Scholar
  27. [DF92a]
    Fellows, M.R.: Fixed parameter tractability and completeness. Congressus Numerantium 87, 161–187 (1992)MathSciNetzbMATHGoogle Scholar
  28. [DF92b]
    Downey, R., Fellows, M.: Fixed parameter intractability. In: Proceedings Structure in Complexity, Seventh Annual Conference, pp. 36–50. IEEE Publication (1992)Google Scholar
  29. [DF93]
    Downey, R., Fellows, M.: Fixed Parameter Tractability and Completeness III: Some Structural Aspects of the W-Hierarchy. In: Ambos-Spies, K., Homer, S., Schöning, U. (eds.) Complexity Theory: Current Research, pp. 166–191. Cambridge Univ. Press (1993)Google Scholar
  30. [DF95a]
    Downey, R.G., Fellows, M.R.: Fixed Parameter Tractability and Completeness I: Basic Theory. SIAM Journal of Computing 24, 873–921 (1995)CrossRefzbMATHGoogle Scholar
  31. [DF95b]
    Downey, R.G., Fellows, M.R.: Fixed Parameter Tractability and Completeness II: Completeness for W[1]. Theoretical Computer Science A 141, 109–131 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  32. [DF95c]
    Downey, R.G., Fellows, M.R.: Parametrized Computational Feasibility. In: Clote, P., Remmel, J. (eds.) Feasible Mathematics II, pp. 219–244. Birkhauser, Boston (1995)CrossRefGoogle Scholar
  33. [DF98]
    Downey, R.G., Fellows, M.: Threshold Dominating Sets and an Improved Characterization of W[2]. Theoretical Computer Science 209, 123–140 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  34. [DF99]
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
  35. [DFta]
    Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer (in preparation, 2012)Google Scholar
  36. [DFS98]
    Downey, R., Fellows, M., Stege, U.: Parameterized Complexity: A Framework for Systematically Confronting Computational Intractability. In: Graham, R., Krachovil, J., Nesetril, J., Roberts, F. (eds.) Contemporary Trends in Discrete Mathematics. DIMACS, vol. 49, pp. 49–100. American Mathematical Society (1999)Google Scholar
  37. [DFS99]
    Downey, R., Fellows, M., Stege, U.: Computational Tractability: the View from Mars. Bulletin of the European Association for Theoretical Computer Science (69), 73–97 (1999)Google Scholar
  38. [DFKHW94]
    Downey, R.G., Fellows, M., Kapron, B., Hallett, M., Wareham, H.T.: The Parameterized Complexity of Some Problems in Logic and Linguistics. In: Matiyasevich, Y.V., Nerode, A. (eds.) LFCS 1994. LNCS, vol. 813, pp. 89–100. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  39. [DFR98]
    Downey, R.G., Fellows, M.R., Regan, K.W.: Parameterized Circuit Complexity and the W Hierarchy. Theoretical Computer Science A 191, 91–115 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  40. [DFT96]
    Downey, R.G., Fellows, M., Taylor, U.: The Parameterized Complexity of Relational Database Queries and an Improved Characterization of W[1]. In: Combinatorics, Complexity and Logic: Proceedings of DMTCS 1996, pp. 194–213. Springer (1997)Google Scholar
  41. [DFVW99]
    Downey, R., Fellows, M., Vardy, A., Whittle, G.: The Parameterized Complexity of Some Fundamental Problems in Coding Theory. SIAM J. Comput. 29, 545–570 (1999)CrossRefzbMATHGoogle Scholar
  42. [DFo03]
    Downey, R., Fortnow, L.: Uniformly hard languages. Theoretical Computer Science 298(2), 303–315 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  43. [DGHM89]
    Downey, R., Gasarch, W., Homer, S., Moses, M.: Honest polynomial reductions, non-relativizations and P = ?NP. In: Proceedings of the 4th Annual Conference on Structures in Complexity Theory, pp. 196–207. IEEE Publ. (1989)Google Scholar
  44. [DH10]
    Downey, R., Hirschfeldt, D.: Algorithmic Randomness and Complexity, pp. xvii+855. Springer (2010)Google Scholar
  45. [DM08]
    Downey, R., Montalbán, A.: The isomorphism problem for torsion-free abelian groups is analytic complete. Journal of Algebra 320, 2291–2300 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  46. [Fe89]
    Fellows, M.R.: The Robertson-Seymour Theorems: a Survey of Applications. In: Contemporary Mathematics, vol. 89, pp. 1–18. AMS (1989)Google Scholar
  47. [FL87]
    Fellows, M.R., Langston, M.: Nonconstructive Proofs of Polynomial-Time Complexity. Information Processing Letters 26(88), 157–162 (1987/1988)MathSciNetCrossRefzbMATHGoogle Scholar
  48. [FL88]
    Fellows, M.R., Langston, M.: Nonconstructive Tools for Proving Polynomial-Time Complexity. Journal of the Association for Computing Machinery 35, 727–739 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  49. [FL89]
    Fellows, M.R., Langston, M.A.: An Analogue of the Myhill-Nerode Theorem and its Use in Computing Finite-Basis Characterizations. In: Proceedings of the IEEE Symposium on the Foundations of Computer Science, pp. 520–525 (1989)Google Scholar
  50. [FL89b]
    Fellows, M.R., Langston, M.A.: On search, decision and nefficiency of polynomial time algorithms. In: Proceedings STOC 1989, pp. 501–512 (1989)Google Scholar
  51. [FK93]
    Fellows, M.R., Koblitz, N.: Fixed-Parameter Complexity and Cryptography. In: Moreno, O., Cohen, G., Mora, T. (eds.) AAECC 1993. LNCS, vol. 673, pp. 121–131. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  52. [FG06]
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)Google Scholar
  53. [GJ79]
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco (1979)zbMATHGoogle Scholar
  54. [GGKS95]
    Goldberg, P., Golumbic, M., Kaplan, H., Shamir, R.: Four Strikes Against DNA Physical mapping. Journal of Computational Biology 2(1), 139–152 (1995)CrossRefGoogle Scholar
  55. [Gr01a]
    Grohe, M.: Generalized Model-Checking Problems for First-Order Logic. In: Ferreira, A., Reichel, H. (eds.) STACS 2001. LNCS, vol. 2010, pp. 12–26. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  56. [Gr01b]
    Grohe, M.: The Parameterized Complexity of Database Queries. In: Proc. PODS 2001, pp. 82–92. ACM Press (2001)Google Scholar
  57. [Gr02]
    Grohe, M.: Parameterized Complexity for the Database Theorist. SIGMOD Record 31(4) (2002)Google Scholar
  58. [IPZ01]
    Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? JCSS 63(4), 512–530 (2001)MathSciNetzbMATHGoogle Scholar
  59. [KW90]
    Kannan, S., Warnow, T.: Inferring Evolutionary History from DNA Sequences. In: Proceedings of the 31st Annual Symposium on the Theory of Computing, pp. 362–378 (1990)Google Scholar
  60. [KST94]
    Kaplan, H., Shamir, R., Tarjan, R.E.: Tractability of Parameterized Completion Problems on Chordal and Interval Graphs: Minimum Fill-In and DNA Physical Mapping. In: Proc. 35th Annual Symposium on the Foundations of Computer Science (FOCS), pp. 780–791. IEEE Press (1994)Google Scholar
  61. [KF80]
    Kintala, C., Fischer, P.: Refining nondeterminism and relativized polynomial time bounded computations. SIAM J. Comput. 9, 46–53 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  62. [KR00]
    Khot, S., Raman, V.: Parameterized Complexity of Finding Subgraphs with Hereditary properties. Theoretical Computer Science 289, 997–1008 (2002); preliminary version in: Du, D.-Z., Eades, P., Sharma, A.K., Lin, X., Estivill-Castro, V. (eds.) COCOON 2000. LNCS, vol. 1858, pp. 137–147. Springer, Heidelberg (2000) Google Scholar
  63. [LPSSV08]
    Langston, M., Perkins, A., Saxton, A., Scharff, J., Voy, B.: Innovative computational methods for transcriptomic data analysis: A case study in the use of FPT for practical algorithm design and implementation. The Computer Journal 51(1), 26–38 (2008)CrossRefGoogle Scholar
  64. [Le83]
    Lenstra, H.: Integer Programming with a Fixed Number of Variables. Mathematics of Operations Research 8, 538–548 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  65. [LP85]
    Lichtenstein, O., Pnueli, A.: Checking that Finite State Concurrent Programs Satisfy their Linear Specification. In: POPL 1985, pp. 97–107 (1985)Google Scholar
  66. [MR99]
    Mahajan, M., Raman, V.: Parameterizing Above Guaranteed Values: MaxSat and MaxCut. J. Algorithms 31, 335–354 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  67. [Ma12]
    Marx, D.: What’s Next? Future Directions in Parameterized Complexity. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 469–496. Springer, Heidelberg (2012)Google Scholar
  68. [Mo99]
    Mohar, B.: A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface. SIAM J. Discrete Math. 12, 6–26 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  69. [Mu08a]
    Müller, M.: Parameterized Derandomization. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 148–159. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  70. [Mu08b]
    Müller, M.: Valiant-vazirani lemmata for various logics. Electronic Colloquium on Computational Complexity (ECCC) 15(063) (2008)Google Scholar
  71. [Nie06]
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
  72. [OW91]
    Ogiwara, M., Watanabe, O.: On Polynomial Bounded Truth-Table Reducibility of NP Sets to Sparse Sets. SICOMP, 471–483 (1991)Google Scholar
  73. [PY91]
    Papadimitriou, C., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. Syst. Sci. 43, 425–440 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  74. [PY93]
    Papadimitriou, C., Yannakakis, M.: On Limited Nondeterminism and the Complexity of the V-C Dimension. In: Eight Annual Conference on Structure in Complexity Theory, pp. 12–18 (1993)Google Scholar
  75. [PY97]
    Papadimitriou, C., Yannakakis, M.: On the Complexity of Database Queries. In: Proc. ACM Symp. on Principles of Database Systems, pp. 12–19 (1997); Journal version in Journal of Computer System Sciences 58, 407–427 (1999)Google Scholar
  76. [ST98]
    Shamir, R., Tzur, D.: The Maximum Subforest Problem: Approximation and Exact Algorithms. In: Proc. ACM Symposium on Discrete Algorithms, SODA 1998, pp. 394–399. ACM Press (1998)Google Scholar
  77. [St00]
    Stege, U.: Resolving Conflicts in Problems in Computational Biochemistry. Ph.D. dissertation, ETH (2000)Google Scholar
  78. [Ra97]
    Raman, V.: Parameterized Complexity. In: Proceedings of the 7th National Seminar on Theoretical Computer Science, Chennai, India, pp. 1–18 (1997)Google Scholar
  79. [Re89]
    Regan, K.: Finite substructure languages. In: Proceedings 4th Structure in Complexity Annual Conference, pp. 87–96 (1989)Google Scholar
  80. [RS86a]
    Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms 7, 309–322 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  81. [VV86]
    Valiant, L., Vazirani, V.: NP is as easy as detecting unique solutions. Theoret. Comput. Sci. 47, 85–93 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  82. [Va82]
    Vardi, M.: The Complexity of Relational Database Queries. In: Proc. STOC, pp. 137–146 (1982)Google Scholar
  83. [VW86]
    Vardi, M., Wolper, P.: An Automata-Theoretic Approach to Automatic Program Verification. In: LICS 1986, pp. 332–344 (1986)Google Scholar
  84. [Va95]
    Vardi, M.: On the complexity of bounded-variable queries. In: PODS 1995 (1995)Google Scholar
  85. [Va09]
    Vardi, M.: Conferences vs. Journals in Computing Research. Communications of the ACM 52(5), 5 (2009)CrossRefGoogle Scholar
  86. [Ya95]
    Yannakakis, M.: Perspectives in Database Theory. In: FOCS, pp. 224–246 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Rod Downey
    • 1
    • 2
  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria UniversityWellingtonNew Zealand
  2. 2.Isaac Newton Institute for Mathematical SciencesCambridgeUnited Kingdom

Personalised recommendations