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Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology

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Combinatorial Algorithms (IWOCA 2009)

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Abstract

This paper reports on three recent research directions that begin to explore the subject of fully multivariate algorithmics, meaning by this the largely uncharted theoretical landscape that lies beyond parameterized complexity and algorithmics — itself a natural two-dimensional generalization of the familiar one-dimensional framework of \(\mathcal{P}\) versus \(\mathcal{NP}\).

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References

  1. Arnborg, S., Lagergren, J., Seese, D.: Easy problems for tree-decomposable graphs. J. Algorithms 12, 308–340 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bodlaender, H., Fellows, M., Hallett, M.: Beyond NP-completeness for problems of bounded width: hardness for the W hierarchy. In: Proceedings of the ACM Symposium on the Theory of Computing (STOC), pp. 449–458 (1994)

    Google Scholar 

  3. Bodlaender, H.L., Koster, A.M.: Combinatorial optimisation on graphs of bounded treewidth. The Computer Journal 51, 255–269 (2007)

    Article  Google Scholar 

  4. Bodlaender, H.L.: A linear time algorithm for finding tree-decompositions of small width. SIAM J. Computing 25, 1305–1317 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Fellows, M., Downey, R., Langston, M. (Guest eds.): The Computer Journal: Two special issues of surveys of various aspects of parameterized complexity and algorithmics. The Computer Journal 51(1&3) (2008)

    Google Scholar 

  7. Courcelle, B.: The monadic second order logic of graphs I: Recognizable sets of finite graphs. Information and Computation 85, 12–75 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ding, G.: Subgraphs and well-quasi-ordering. J. Graph Theory 16, 489–502 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. Downey, R., Estivill-Castro, V., Fellows, M., Prieto-Rodriguez, E., Rosamond, F.: Cutting up is hard to do: the parameterized complexity of k-cut and related problems. Electron. Notes Theor. Comp. Sci. 78, 205–218 (2003)

    Google Scholar 

  10. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  11. Downey, R., Fellows, M., Hallett, M., Kapron, B., 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)

    Google Scholar 

  12. Parameterized approximation for dominating set problems. Information Processing Letters 109, 68–70 (2008)

    Google Scholar 

  13. Downey, R., Fellows, M., Stege, U.: Parameterized complexity: a framework for systematically confronting computational intractability. In: Graham, R., Kratochvil, J., Nesetril, J., Roberts, F. (eds.) Contemporary Trends in Discrete Mathematics, Proceedings of the DIMACS-DIMATIA Workshop on the Future of Discrete Mathematics, Prague, 1997. AMS-DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 49, pp. 49–99 (1999)

    Google Scholar 

  14. Fellows, M., Fomin, F., Lokshtanov, D., Rosamond, F., Saurabh, S., Szeider, S., Thomassen, C.: On the complexity of some colorful problems parameterized by treewidth. In: Dress, A.W.M., Xu, Y., Zhu, B. (eds.) COCOA 2007. LNCS, vol. 4616, pp. 366–377. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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

    Google Scholar 

  16. Fellows, M., Hermelin, D., Rosamond, F.: Well-quasi-ordering bounded treewidth graphs. In: Proceedings of IWPEC 2009. LNCS, vol. 5917. Springer, Heidelberg (to appear)

    Google Scholar 

  17. Fellows, M., Hermelin, D., Rosamond, F.: Parameter ecology, well-quasi-ordering and universal antichains (manuscript, 2009)

    Google Scholar 

  18. Fellows, M., Lokshtanov, D., Misra, N., Rosamond, F., Saurabh, S.: Graph Layout Problems Parameterized by Vertex Cover. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 294–305. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Fellows, M., Lokshtanov, D., Misra, N., Mnich, M., Rosamond, F., Saurabh, S.: The complexity ecology of parameters: an illustration using bounded max leaf number. Theory of Computing Systems (2009)

    Google Scholar 

  20. Henglein, F., Mairson, H.G.: The complexity of type inference for higher-order typed lambda calculi. In: Proc. Symp. on Principles of Programming Languages (POPL), pp. 119–130. ACM Press, New York (1991)

    Google Scholar 

  21. Impagliazzo, R., Paturi, R.: Which problems have strongly exponential complexity? J. Computer and Systems Sciences 63, 512–530 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lichtenstein, O., Pneuli, A.: Checking That Finite-State Concurrents Programs Satisfy Their Linear Specification. In: Proceedings of the 12th ACM Symposium on Principles of Programming Languages, pp. 97–107 (1985)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  24. Robertson, N., Seymour, P.: Graph minors: a survey. In: Anderson, J. (ed.) Surveys in Combinatorics, pp. 153–171. Cambridge University Press, Cambridge (1985)

    Google Scholar 

  25. Robertson, N., Seymour, P.: Graph minors XX. Wagner’s conjecture. J. Comb. Th. Series B 92, 325–357 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  26. Szeider, S.: Monadic second order logic on graphs with local cardinality constraints. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 601–612. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Szeider, S.: Not so easy problems for tree decomposable graphs. In: Proc. ICDM 2008 (to appear)

    Google Scholar 

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Fellows, M. (2009). Towards Fully Multivariate Algorithmics: Some New Results and Directions in Parameter Ecology. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-10217-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10216-5

  • Online ISBN: 978-3-642-10217-2

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