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Komplexitätstheorie

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Exakte Algorithmen für schwere Graphenprobleme

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Zusammenfassung

Wann ist ein Problem schwer? Warum ist ein Problem schwerer als ein anderes? Mit diesen Fragen befasst sich die Komplexitätstheorie. In Abschnitt 3.4 wurden ausgewählte Graphenprobleme vorgestellt, wie zum Beispiel das Färbbarkeitsproblem für Graphen, und es wurde erwähnt, dass alle diese Probleme „schwer“ sind. Was darunter zu verstehen ist, wird Inhalt dieses Kapitels sein.

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References

  1. R. Stearns. Juris Hartmanis: The beginnings of computational complexity. In A. Selman, editor, Complexity Theory Retrospective, pages 1–18. Springer-Verlag, 1990.

    Google Scholar 

  2. L. Stockmeyer. The polynomial-time hierarchy. Theoretical Computer Science, 3(1):1–22, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Rothe. Komplexitätstheorie und Kryptologie. Eine Einführung in Kryptokomplexität. eXamen.Press. Springer-Verlag, 2008.

    Google Scholar 

  4. J. Flum and M. Grohe. Parameterized Complexity Theory. EATCS Texts in Theoretical Computer Science. Springer-Verlag, 2006.

    Google Scholar 

  5. J. Edmonds. Paths, trees and flowers. Canadian Journal of Mathematics, 17:449–467, 1965.

    MATH  MathSciNet  Google Scholar 

  6. L. Levin. Universal sorting problems. Problemy Peredaci Informacii, 9:115–116, 1973. In Russian. English translation in Problems of Information Transmission, 9:265–266, 1973.

    Google Scholar 

  7. R. Downey and M. Fellows. Parameterized Complexity. Springer-Verlag, 1999.

    Google Scholar 

  8. A. Cobham. The intrinsic computational difficulty of functions. In Proceedings of the 1964 International Congress for Logic Methodology and Philosophy of Science, pages 24–30. North Holland, 1964.

    Google Scholar 

  9. R. Karp. Reducibilities among combinatorial problems. In R. Miller and J. Thatcher, editors, Complexity of Computer Computations, pages 85–103, 1972.

    Google Scholar 

  10. S. Cook. The complexity of theorem-proving procedures. In Proceedings of the 3rd ACM Symposium on Theory of Computing, pages 151–158. ACM Press, 1971.

    Google Scholar 

  11. K. Wagner. More complicated questions about maxima and minima, and some closures of NP. Theoretical Computer Science, 51:53–80, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Wrathall. Complete sets and the polynomial-time hierarchy. Theoretical Computer Science, 3:23–33, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  13. C. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

    Google Scholar 

  14. L. Stockmeyer. Planar 3-colorability is NP-complete. SIGACT News, 5(3):19–25, 1973.

    Article  Google Scholar 

  15. D. Bovet and P. Crescenzi. Introduction to the Theory of Complexity. Prentice Hall, 1993.

    Google Scholar 

  16. M. Schaefer and C. Umans. Completeness in the polynomial-time hierarchy: PartI: A compendium. SIGACT News, 33(3):32–49, September 2002.

    Article  Google Scholar 

  17. R. Niedermeier. Invitation to Fixed-Parameter Algorithms. Oxford University Press, 2006.

    Google Scholar 

  18. W. Savitch. Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences, 4(2):177–192, 1970.

    MATH  MathSciNet  Google Scholar 

  19. A. Rosenberg. Real-time definable languages. Journal of the ACM, 14:645–662, 1967.

    Article  MATH  Google Scholar 

  20. C. Papadimitriou. On the complexity of unique solutions. Journal of the ACM, 31(2):392–400, 1984.

    Article  MathSciNet  Google Scholar 

  21. A. Meyer and L. Stockmeyer. The equivalence problem for regular expressions with squaring requires exponential space. In Proceedings of the 13th IEEE Symposium on Switching and Automata Theory, pages 125–129. IEEE Computer Society Press, October 1972.

    Google Scholar 

  22. T. Schaefer. The complexity of satisfiability problems. In Proceedings of the 10th ACM Symposium on Theory of Computing, pages 216–226. ACM Press, May 1978.

    Google Scholar 

  23. J. Hartmanis, P. Lewis, and R. Stearns. Classification of computations by time and memory requirements. In Proceedings of the IFIP World Computer Congress 65, pages 31–35. International Federation for Information Processing, Spartan Books, 1965.

    Google Scholar 

  24. J. Hartmanis and R. Stearns. On the computational complexity of algorithms. Transactions of the American Mathematical Society, 117:285–306, 1965.

    MATH  MathSciNet  Google Scholar 

  25. K. Appel and W. Haken. Every planar map is 4-colorable – 1: Discharging. Illinois J. Math, 21:429–490, 1977.

    MATH  MathSciNet  Google Scholar 

  26. S. Khuller and V. Vazirani. Planar graph coloring is not self-reducible, assuming \({\textrm{p}} \neq {\textrm{np}}\). Theoretical Computer Science, 88(1):183–189, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  27. J. Rothe. Complexity Theory and Cryptology. An Introduction to Cryptocomplexity. EATCS Texts in Theoretical Computer Science. Springer-Verlag, 2005.

    Google Scholar 

  28. R. Downey and M. Fellows. Fixed parameter tractability and completeness. Congressus Numerantium, 87:161–187, 1992.

    MathSciNet  Google Scholar 

  29. R. Stearns, J. Hartmanis, and P. Lewis. Hierarchies of memory limited computations. In Proceedings of the 6th IEEE Symposium on Switching Circuit Theory and Logical Design, pages 179–190. IEEE Computer Society Press, October 1965.

    Google Scholar 

  30. P. Lewis, R. Stearns, and J. Hartmanis. Memory bounds for recognition of context-free and context-sensitive languages. In Proceedings of the 6th IEEE Symposium on Switching Circuit Theory and Logical Design, pages 191–202. IEEE Computer Society Press, October 1965.

    Google Scholar 

  31. M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, 1979.

    Google Scholar 

  32. C. Umans. The minimum equivalent DNF problem and shortest implicants. Journal of Computer and System Sciences, 63(4):597–611, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  33. M. Krentel. The complexity of optimization problems. Journal of Computer and System Sciences, 36:490–509, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  34. J. Balcázar, J.Díaz, and J. Gabarró. Structural Complexity II. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1990.

    Google Scholar 

  35. J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, second edition, 1995.

    Google Scholar 

  36. A. Groβe, J. Rothe, and G. Wechsung. On computing the smallest four-coloring of planar graphs and non-self-reducible sets in P. Information Processing Letters, 99(6):215–221, 2006.

    Article  MathSciNet  Google Scholar 

  37. R. Downey and M. Fellows. Fixed-parameter tractability and completeness I: Basic results. SIAM Journal on Computing, 24(4):873–921, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  38. R. Fagin. Generalized first-order spectra and polynomial-time recognizable sets. In R. Karp, editor, Complexity of Computation, volume7, pages 43–73. Proceedings of the SIAM-AMS Symposium in Applied Mathematics, 1974.

    Google Scholar 

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Correspondence to Frank Gurski .

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Gurski, F., Rothe, I., Rothe, J., Wanke, E. (2010). Komplexitätstheorie. In: Exakte Algorithmen für schwere Graphenprobleme. eXamen.press. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04500-4_5

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