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International Workshop on Parameterized and Exact Computation

IWPEC 2004: Parameterized and Exact Computation pp 162–173Cite as

A Structural View on Parameterizing Problems: Distance from Triviality

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3162))

Abstract

Based on a series of known and new examples, we propose the generalized setting of “distance from triviality” measurement as a reasonable and prospective way of determining useful structural problem parameters in analyzing computationally hard problems. The underlying idea is to consider tractable special cases of generally hard problems and to introduce parameters that measure the distance from these special cases. In this paper we present several case studies of distance from triviality parameterizations (concerning Clique, Power Dominating Set, Set Cover, and Longest Common Subsequence) that exhibit the versatility of this approach to develop important new views for computational complexity analysis.

Supported by the Deutsche Forschungsgemeinschaft (DFG), Emmy Noether research group PIAF (fixed-parameter algorithms), NI 369/4.

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References

  1. Alber, J., Bodlaender, H.L., Fernau, H., Kloks, T., Niedermeier, R.: Fixed parameter algorithms for Dominating Set and related problems on planar graphs. Algorithmica 33(4), 461–493 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alber, J., Fan, H., Fellows, M.R., Fernau, H., Niedermeier, R., Rosamond, F., Stege, U.: Refined search tree technique for Dominating Set on planar graphs. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 111–122. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Bodlaender, H.L.: Classes of graphs with bounded treewidth. Technical Report RUU-CS-86-22, Dept. of Computer Sci., Utrecht University (1986)

    Google Scholar 

  4. Bodlaender, H.L.: Treewidth: Algorithmic techniques and results. In: Privara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 19–36. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  5. Bodlaender, H.L., Downey, R.G., Fellows, M.R., Wareham, H.T.: The parameterized complexity of the longest common subsequence problem. Theoretical Computer Science 147, 31–54 (1995)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Cai, L.: Parameterized complexity of Vertex Colouring. Discrete Applied Mathematics 127(1), 415–429 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chen, J., Kanj, I.A., Jia, W.: Vertex Cover: Further observations and further improvements. J. Algorithms 41, 280–301 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Demaine, E.D., Fomin, F.V., Hajiaghayi, M.T., Thilikos, D.M.: Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs. In: Proc. 15th SODA, pp. 830–839. SIAM, Philadelphia (2004)

    Google Scholar 

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

    Google Scholar 

  11. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999); 4 The latter being of particular interest when attacking W[1]-hard problems

    Google Scholar 

  12. Ellis, J., Fan, H., Fellows, M.R.: The Dominating Set problem is fixed parameter tractable for graphs of bounded genus. In: Penttonen, M., Schmidt, E.M. (eds.) SWAT 2002. LNCS, vol. 2368, pp. 180–189. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Fellows, M.R.: Blow-ups, win/win’s, and crown rules: Some new directions in FPT. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 1–12. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Fellows, M.R.: New directions and new challenges in algorithm design and complexity, parameterized. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 505–520. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Fixed-parameter algorithms for clique generation. In: CIAC 2003. LNCS, vol. 2653, pp. 108–119. Springer, Heidelberg (2003); To appear in Theory of Computing Systems.

    Google Scholar 

  16. Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4), 321–347 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Guo, J., Niedermeier, R.: Exact algorithms and applications for Tree-like Weighted Set Cover (June 2004) (manuscript)

    Google Scholar 

  18. Haynes, T.W., Hedetniemi, S.M., Hedetniemi, S.T., Henning, M.A.: Domination in graphs applied to electric power networks. SIAM J. Discrete Math. 15(4), 519–529 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Hoffmann, M., Okamoto, Y.: The traveling salesman problem with few inner points. In: Chwa, K.-Y., Munro, J.I.J. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 268–277. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Juedes, D., Chor, B., Fellows, M.R.: Linear kernels in linear time, or How to save k colors in O(n2) steps. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 257–269. Springer, Heidelberg (2004) (to appear)

    Chapter  Google Scholar 

  21. Niedermeier, R.: Ubiquitous parameterization—invitation to fixed-parameter algorithms. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 84–103. Springer, Heidelberg (2004) (to appear)

    Chapter  Google Scholar 

  22. Niedermeier, R., Rossmanith, P.: On efficient fixed-parameter algorithms for Weighted Vertex Cover. J. Algorithms 47(2), 63–77 (2003)

    MATH  MathSciNet  Google Scholar 

  23. Nishimura, N., Ragde, P., Thilikos, D.M.: Fast fixed-parameter tractable algorithms for nontrivial generalizations of Vertex Cover. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 75–86. Springer, Heidelberg (2001); To appear in Discrete Applied Mathematics

    Chapter  Google Scholar 

  24. Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. Syst. Sci. 43, 425–440 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  25. Pietrzak, K.: On the parameterized complexity of the fixed alphabet Shortest Common Supersequence and Longest Common Subsequence problems. J. Comput. Syst. Sci. 67(4), 757–771 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  26. Robertson, N., Seymour, P.D.: Graph minors. II: Algorithmic aspects of treewidth. J. Algorithms 7, 309–322 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  27. Robson, J.M.: Algorithms for maximum independent sets. J. Algorithms 7, 425–440 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  28. Szeider, S.: Minimal unsatisfiable formulas with bounded clause-variable difference are fixed-parameter tractable. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 548–558. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  29. Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13(3), 566–579 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  30. Telle, J.A., Proskurowski, A.: Practical algorithms on partial k-trees with an application to domination-like problems. In: Dehne, F., Sack, J.-R., Santoro, N. (eds.) WADS 1993. LNCS, vol. 709, pp. 610–621. Springer, Heidelberg (1993)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Fed. Rep. of Germany

    Jiong Guo, Falk Hüffner & Rolf Niedermeier

Authors
  1. Jiong Guo
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  2. Falk Hüffner
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  3. Rolf Niedermeier
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Editor information

Editors and Affiliations

  1. School of Mathematics, Statistics, and Computer Science, Victoria University, PO Box 600, Wellington, New Zealand

    Rod Downey

  2. PCRU, Office of DVC (Research), University of Newcastle, Australia

    Michael Fellows

  3. Carleton University, Ottawa, Canada

    Frank Dehne

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Guo, J., Hüffner, F., Niedermeier, R. (2004). A Structural View on Parameterizing Problems: Distance from Triviality. In: Downey, R., Fellows, M., Dehne, F. (eds) Parameterized and Exact Computation. IWPEC 2004. Lecture Notes in Computer Science, vol 3162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28639-4_15

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  • DOI: https://doi.org/10.1007/978-3-540-28639-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23071-7

  • Online ISBN: 978-3-540-28639-4

  • eBook Packages: Springer Book Archive

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