Skip to main content
Springer Nature Link
Log in

A Basic Parameterized Complexity Primer

  • Chapter
The Multivariate Algorithmic Revolution and Beyond

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7370))

Abstract

This article was prepared for Mike Fellows Festschrift for his 60th Birthday. Since many of the contributed articles revolve around the concept of parameterized complexity, it seems reasonable to give the reader a (short) primer to this area. It is not intended as a complete survey of this very broad area in its current state; rather it is intended to give a flavour of the techniques used and the directions taken. Whilst not doing the area justice, the basics of the techniques for proving tractability, establishing hardness, and the philosophy are given. The basics from this paper will be amplified by many other articles in this Festschrift. Much fuller accounts can be found in the books Downey-Fellows [DF98, DFta], Niedermeier [Nie06], Flum-Grohe [FG06], the two issues of the Computer Journal[DFL08] and the recent survey Downey-Thilikos [DTH11].

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Abu-Khzam, F., Collins, R.L., Fellows, M.R., Langston, M.A., Suters, W.H., Symons, C.T.: Kernelization Algorithms for the Vertex Cover Problem: Theory and Experiments. In: Proceedings of the 6th ALENEX 2004, pp. 62–69 (2004)

    Google Scholar 

  2. Abu-Khzam, F., Fellows, M., Langston, M., Suters, W.: Crown Structures for Vertex Cover Kernelization. Theory Comput. Syst. 41(3), 411–430 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abu-Khzam, F., Langston, M., Shanbhag, P., Symons, C.: Scalable Parallel Algorithms for FPT Problems. Algorithmica 45, 269–284 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Abrahamson, K., Downey, R., Fellows, M.: Fixed Parameter Intractability II (Extended Absrtact). In: Enjalbert, P., Wagner, K.W., Finkel, A. (eds.) STACS 1993. LNCS, vol. 665, pp. 374–385. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  5. 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)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. Adler, I., Grohe, M., Kreutzer, S.: Computing excluded minors. In: Proceedings of the of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2008), pp. 641–650 (2008)

    Google Scholar 

  8. 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 

  9. 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 

  10. Arora, S.: Polynomial Time Approximation Schemes for Euclidean TSP and Other Geometric Problems. In: Proceedings of the 37th IEEE Symposium on Foundations of Computer Science, pp. 2–12 (1996)

    Google Scholar 

  11. Arora, S.: Nearly Linear Time Approximation Schemes for Euclidean TSP and Other Geometric Problems. In: Proc. 38th Annual IEEE Symposium on the Foundations of Computing (FOCS 1997), pp. 554–563. IEEE Press (1997)

    Google Scholar 

  12. Bazgan, C.: Schémas d’approximation et complexité paramétrée, Rapport de stage de DEA d’Informatique à Orsay (1995)

    Google Scholar 

  13. Betzler, N., Bredereck, R., Chen, J., Niedermeier, R.: Studies in Computational Aspects of Voting – a Parameterized Complexity Perspective. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 318–363. Springer, Heidelberg (2012)

    Google Scholar 

  14. Bienstock, D., Langston, M.: Algorithmic Implications of the Graph Minor Theorem. In: Ball, M.O., Magnanti, T.L., Monma, C.L., Nemhauser, G.L. (eds.) Handbook of Operations Research and Management Science: Network Models, pp. 481–502. North Holland (1995)

    Google Scholar 

  15. 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 

  16. Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Bodlaender, H.L.: Fixed-Parameter Tractability of Treewidth and Pathwidth. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 196–227. Springer, Heidelberg (2012)

    Google Scholar 

  18. Bodlaender, H.L., 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)

    Chapter  Google Scholar 

  19. Bodlaender, H.L., Downey, R., Fellows, M., Hermelin, D.: On Problems without Polynomial Kernels. Journal of Computing and System Sciences 75(8), 423–434 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Bodlaender, H.L., 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 

  21. Bodlaender, H.L., 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 

  22. Bodlaender, H.L., Fomin, F., Lokshtanov, D., Pennick, E., Saurabh, S., Thilikos, D.: (Meta)kernelization. In: 50th IEEE FOCS (2009)

    Google Scholar 

  23. Bodlaender, H.L., Kloks, T.: Efficient and constructive algorithms for the pathwidth and treewdith of graphs. Algorithms 21, 358–402 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  24. Bodlaender, H.L., Koster, A.: Combinatorial optimization on graphs of bounded treewidth. The Computer Journal 51, 256–269 (2008)

    Google Scholar 

  25. Bodlaender, H.L., Thomasse, S., Yeo, A.: Analysis of data reduction, transformations give evidence for non-existence of polynomial kernels, Tech. Rept, UU-CS-2008-030, Utrecht Univ. (2008)

    Google Scholar 

  26. Bonnet, M., Pitazzi, T., Raz, R.: On Interpolation and Axiomatization for Frege Systems. SIAM J. Comput. 29, 1939–1967 (2000)

    Article  Google Scholar 

  27. Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters 58(4), 171–176 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  28. Cai, L., Chen, J.: On Fixed-Parameter Tractability and Approximability of NP-Hard Optimization Problems. Computer and Systems Sciences 54, 465–474 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  29. 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)

    Article  MathSciNet  MATH  Google Scholar 

  30. Cai, L., Fellows, M., Juedes, D., Rosamond, F.: The complexity of polynomial time approximation. Theoretical Computer Science 41, 459–477 (2007)

    MathSciNet  MATH  Google Scholar 

  31. Cai, L., Juedes, D.W.: Subexponential Parameterized Algorithms Collapse the W-Hierarchy. In: Yu, Y., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 273–284. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  32. Cai, L., Juedes, D.W.: On the existence of subexponential parameterized algorithms. Journal of Computing snd Systems Science 67, 789–807 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  33. Cheetham, J., Dehne, F., Rau-Chaplin, A., Stege, U., Taillon, P.J.: Solving Large FPT Problems on Coarse Grained Parallel Machines. Journal of Computer and Systems Sciences 67(4), 691–706 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  34. Chekuri, C., Khanna, S.: A PTAS for the Multiple Knapsack Problem. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA 2000), pp. 213–222 (2000)

    Google Scholar 

  35. Chen, J., Chor, B., Fellows, M., Huang, X., Juedes, D.W., Kanj, A., Xia, G.: Tight lower bounds for certain parameterized NP-hard problems. Information and Computation 201, 216–231 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  36. Chen, Y., Flum, J., Müller, M.: Lower Bounds for Kernelizations and Other Preprocessing Procedures. Theory Comput. Syst. 48(4), 803–839 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  37. Chen, J., Kanj, I.: Parameterized Complexity and Subexponential-Time Computability. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 162–195. Springer, Heidelberg (2012)

    Google Scholar 

  38. Chen, J., Miranda, A.: A Polynomial-Time Approximation Scheme for General Multiprocessor Scheduling. In: Proc. ACM Symposium on Theory of Computing (STOC 1999), pp. 418–427. ACM Press (1999)

    Google Scholar 

  39. Chen, J., Kanj, I.A., Xia, G.: Improved upper bounds for vertex cover. Theor. Comput. Sci. 411, 3736–3756 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  40. Chen, J., Flum, J.: A Parameterized Halting Problem. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 364–397. Springer, Heidelberg (2012)

    Google Scholar 

  41. Chen, J., Grohe, M.: An isomorphism between subexponential and parameterized complexity theory. SIAM. J. Comput. 37, 1228–1258 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  42. Courcelle, B.: Recognizability and Second-Order Definability for Sets of Finite Graphs, Technical Report I-8634, Universite de Bordeaux (1987)

    Google Scholar 

  43. Courcelle, B., Downey, R.G., 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)

    MathSciNet  MATH  Google Scholar 

  44. Demaine, E., Hajiaghayi, M.: The Bidimensionality Theory and Its Algorithmic Applications. Comput. J. 51(3), 292–302 (2008)

    Article  Google Scholar 

  45. Downey, R.G.: Parameterized complexity for the skeptic. In: 18th Annual Conference on Computational Complexity, pp. 147–169. IEEE (2003)

    Google Scholar 

  46. Downey, R.: The Birth and Early Years of Parameterized Complexity. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 17–38. Springer, Heidelberg (2012)

    Google Scholar 

  47. Fellows, M.R.: Fixed parameter tractability and completeness. Congressus Numerantium 87, 161–187 (1992)

    MathSciNet  MATH  Google Scholar 

  48. Downey, R.G, Fellows, M.: Fixed parameter intractability. In: Proceedings of Seventh Annual Conference on Structure in Complexity. IEEE Publication, pp. 36–50 (1992)

    Google Scholar 

  49. Downey, R.G, 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 

  50. Downey, R.G., Fellows, M.R.: Fixed Parameter Tractability and Completeness I: Basic Theory. SIAM Journal of Computing 24, 873–921 (1995)

    Article  MATH  Google Scholar 

  51. Downey, R.G., Fellows, M.R.: Fixed Parameter Tractability and Completeness II: Completeness for W[1]. Theoretical Computer Science A 141, 109–131 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  52. Downey, R.G., Fellows, M.R.: Parametrized Computational Feasibility. In: Clote, P., Remmel, J. (eds.) Feasible Mathematics II, pp. 219–244. Birkhauser, Boston (1995)

    Chapter  Google Scholar 

  53. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1998)

    Google Scholar 

  54. Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Springer (2012) (in preparation)

    Google Scholar 

  55. Downey, R.G., Fellows, M., Langston, M.: Two special issue of The Computer Journal devoted to Parameterized Complexity 58(1,3) (2008)

    Google Scholar 

  56. 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)

    Chapter  Google Scholar 

  57. Downey, R.G., Fellows, M., McCartin, C., Rosamond, F.: Parameterized approximation of dominating set problems. Information Processing Letters 109(1), 68–70 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  58. Downey, R.G., Fellows, M., Regan, K.: Parameterized circuit complexity and the W-hierarchy. Theoretical Computer Science 191, 97–115 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  59. Downey, R.G., Fellows, M., Stege, U.: Parameterized Complexity: A Framework for Systematically Confronting Computational Intractability. DIMACS series on Combinatorics in the 21st Century. AMS Publ. (1998)

    Google Scholar 

  60. Downey, R., Flum, J., Grohe, M., Weyer, M.: Bounded fixed-parameter tractability and reducibility. Annals of Pure and Applied Logic 148, 1–19 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  61. Downey, R.G., Thilikos, D.: Confronting intractability via parameters. Computer Science Review 5, 279–317 (2011)

    Article  MATH  Google Scholar 

  62. Eblen, J.D., Langston, M.A., Rogers, G.L., Weerapurage, D.P.: Parallel Vertex Cover: A Case Study in Dynamic Load Balancing. In: Proceedings of Australasian Symposium on Parallel and Distributed Computing, Perth, Australia (January 2011)

    Google Scholar 

  63. Edmonds, J.: Paths, trees and flowers. Canadian J. Math. 17, 449–467 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  64. Eickmeyer, K., Grohe, M., Grüber, M.: Approximation of Natural W[P]-Complete Minimisation Problems Is Hard. In: IEEE Conference on Computational Complexity, pp. 8–18 (2008)

    Google Scholar 

  65. Erlebach, T., Jansen, K., Seidel, E.: Polynomial Time Approximation Schemes for Geometric Graphs. In: Proc. ACM Symposium on Discrete Algorithms (SODA 2001), pp. 671–679 (2001)

    Google Scholar 

  66. Fellows, M., Langston, M.: Nonconstructive Proofs of Polynomial-Time Complexity. Information Processing Letters 26, 157–162 (1987/1988)

    Article  MathSciNet  MATH  Google Scholar 

  67. Fellows, M., Langston, M.: Nonconstructive Tools for Proving Polynomial-Time Complexity. Journal of the Association for Computing Machinery 35, 727–739 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  68. 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 

  69. Fellows, M., Rosamond, F., Rotics, U., Szeider, S.: Cliquewidth minimization is NP-hard. In: Proceedings STOC 2006, pp. 354–362 (2006)

    Google Scholar 

  70. Fellows, M., Rosamond, F., Rotics, U., Szeider, S.: Cliquewidth NP-complete. SIAM J. on Discrete Mathematics 23, 909–939 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  71. Flum, J., Grohe, M.: Describing Parameterized Complexity Classes. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 359–371. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  72. Flum, J., Grohe, M.: The Parameterized Complexity of Counting Problems. In: Conference version appeared in Proceedings of the 43rd IEEE Symposium on Foundations of Comupter Science (FOCS 2002), pp. 538–547 (2002)

    Google Scholar 

  73. Flum, J., Grohe, M.: Parameterized Complexity and Subexponential Time. Bulletin of the European Association for Theoretical Computer Science 84 (October 2004)

    Google Scholar 

  74. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)

    Google Scholar 

  75. de Fluiter, B.: Algorithms for graphs of small treewidth, PhD Thesis, Utrecht Univ. (1970)

    Google Scholar 

  76. Fomin, F., Golovach, P., Lokshtanov, D., Saurabh, S.: Intractability of Clique-Width Parameterizations. SIAM J. Comput. 39(5), 1941–1956 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  77. Fortnow, L., Santhanam, R.: Infeasible instances of compression and sucinct pcp’s. Journal of Computing and System Sciences 77, 91–106 (2011)

    Article  MATH  Google Scholar 

  78. Frick, M., Grohe, M.: Deciding First Order Properties of Locally Tree-Decomposable Structures. J. ACM 48, 1184–1206 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  79. Frick, M., Grohe, M.: The Complexity of First-Order and Monadic Second-Order Logic Revisited. In: LICS, pp. 215–224 (2002)

    Google Scholar 

  80. Fouhy, J.: Computational Experiments on Graph Width Metrics, MSc Thesis, Victoria University, Wellington (2003)

    Google Scholar 

  81. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  82. Gaspers, S., Szeider, S.: Backdoors to Satisfaction. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 287–317. Springer, Heidelberg (2012)

    Google Scholar 

  83. Goldberg, P., Golumbic, M., Kaplan, H., Shamir, R.: Four Strikes Against DNA Physical mapping. Journal of Computational Biology 2(1), 139–152 (1995)

    Article  Google Scholar 

  84. Gramm, J., Niedermeier, R., Rossmanith, P.: Exact Solutions for Closest String and Related Problems. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 441–453. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  85. 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)

    Chapter  Google Scholar 

  86. Grohe, M., Kreutzer, S.: Methods for Algorithmic Meta Theorems. In: Grohe, M., Makowsky, J. (eds.) Model Theoretic Methods in Finite Combinatorics. Contemporary Mathematics, vol. 558. American Mathematical Society (2011)

    Google Scholar 

  87. Grohe, M., Marx, D., Kawarbayashi, K., Wollan, P.: Finding Topological Subgraphs is Fixed-Parameter Tractable. In: Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC 2011), pp. 479–488 (2011)

    Google Scholar 

  88. Gutin, G., Yeo, A.: Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey. In: Bodlaender, H.L., et al. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 257–286. Springer, Heidelberg (2012)

    Google Scholar 

  89. Hallett, M., McCartin, C.: A Faster FPT Algorithm for the Maximum Agreement Forest Problem. Theory of Computing Systems 41(3) (2007)

    Google Scholar 

  90. Hermelin, D., Kratsch, S., Soltys, K., Whalstrom, M., Wu, X.: Hierarchies of inefficient kernelization (to appear)

    Google Scholar 

  91. Higman, G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 2, 326–336 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  92. Hlineny, P., Whittle, G.: Matroid tree-width. Eur. J. Comb. 27(7), 1117–1128 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  93. Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? JCSS 63(4), 512–530 (2001)

    MathSciNet  MATH  Google Scholar 

  94. 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 

  95. 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 

  96. Karp, R.: Reducibility Among Combinatorial Problems. In: Complexity of Computer Computations, pp. 85–103 (1972)

    Google Scholar 

  97. Karp, R.: Heuristic algorithms in computational molecular biology. J. Comput. Syst. Sci. 77(1), 122–128 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  98. Khot, S., Raman, V.: Parameterized Complexity of Finding Subgraphs with Hereditary properties. Theoretical Computer Science 289, 997–1008 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  99. Koblitz, N.: Crypto Galore! In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 39–50. Springer, Heidelberg (2012)

    Google Scholar 

  100. Kuratowski, K.: Sur le probleme des courbes gauches en topologie. Fund. Math. 15, 271–283 (1930)

    MATH  Google Scholar 

  101. Langston, M.: Fixed-Parameterized Tractability, a Prehistory. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 3–16. Springer, Heidelberg (2012)

    Google Scholar 

  102. 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, 26–38 (2008)

    Article  Google Scholar 

  103. Lenstra, H.: Integer Programming with a Fixed Number of Variables. Mathematics of Operations Research 8, 538–548 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  104. Lokshtanov, D., Misra, N., Saurabh, S.: Kernelization – Preprocessing with A Guarantee. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 129–161. Springer, Heidelberg (2012)

    Google Scholar 

  105. Mahajan, M., Raman, V.: Parameterizing Above Guaranteed Values: MaxSat and MaxCut. J. Algorithms 31, 335–354 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  106. 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 

  107. McCartin, C.: Parameterized counting problems. Annals of Pure and Applied Logic 138, 147–182 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  108. Mohar, B.: A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface. SIAM J. Discrete Math. 12, 6–26 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  109. Müller, M.: Randomized Approximations of Parameterized Counting Problems. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 50–59. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  110. Müller, M.: Valiant-Vazirani Lemmata for Various Logics. Electronic Colloquium on Computational Complexity (ECCC) 15(063) (2008)

    Google Scholar 

  111. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Habilitationschrift, University of Tübingen (September 2002)

    Google Scholar 

  112. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)

    Google Scholar 

  113. Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter tractable algorithms. Information Processing Letters 73, 125–129 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  114. Nemhauser, G., Trotter Jr., L.: Vertex packings: Structural properties and algorithms. Mathematical Programming 8, 232–248 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  115. 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 

  116. Shamir, R., Tzur, D.: The Maximum Subforest Problem: Approximation and Exact Algorithms. In: Proc. ACM Symposium on Discrete Algorithms, pp. 394–399. ACM Press (1998)

    Google Scholar 

  117. Stege, U.: Resolving Conflicts in Problems in Computational Biochemistry. Ph.D. dissertation, ETH (2000)

    Google Scholar 

  118. Stege, U.: The Impact of Parameterized Complexity to Interdisciplinary Problem Solving. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 56–68. Springer, Heidelberg (2012)

    Google Scholar 

  119. Reed, B., Smith, K., Vetta, A.: Finding odd cycle transversals. Operations Research Letters 32, 299–301 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  120. Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms 7, 309–322 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  121. Thilikos, D.: Graph Minors and Parameterized Algorithm Design. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds.) Fellows Festschrift. LNCS, vol. 7370, pp. 228–256. Springer, Heidelberg (2012)

    Google Scholar 

  122. Wagner, K.: Uber einer eigenshaft der eberner complexe. Math. Ann. 14, 570–590 (1937)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Statistics and Operations Research, Victoria University, P.O. Box 600, Wellington, New Zealand

    Rod Downey

Authors
  1. Rod Downey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. School of Mathematics, Statistics and Operations Research, Victoria University, P.O. Box 600, Wellington, New Zealand

    Rod Downey

  3. Institute of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Fedor V. Fomin

  4. Computer and Automation Research Institute, Hungarian Academy of Sciences (MTA SZTAKI), Pf. 63, 1518, Budapest, Hungary

    Dániel Marx

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Downey, R. (2012). A Basic Parameterized Complexity Primer. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds) The Multivariate Algorithmic Revolution and Beyond. Lecture Notes in Computer Science, vol 7370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30891-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30891-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30890-1

  • Online ISBN: 978-3-642-30891-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics