Advertisement

On the formal aspects of approximation algorithms

  • José D. P. Rolim
Theory Of Computing, Algorithms And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 468)

Abstract

Formal aspects of approximated solutions to difficult problems are considered. We define an approximation machine and its language as a formal model of computation. We strengthen previous results by showing the interpretation of the complexity classes with density in terms of approximation languages. In particular, we analyze the worst-case, the best-case and the average-case complexity related to the formal languages of approximation machines. The relationship between density of a complexity class and the “goodness” of an approximation is also investigated.

Keywords

Turing Machine Complexity Class Information Processing Letter Polynomial Optimization Problem Deterministic Turing Machine 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    S. Ben-David, B. Chor, O. Goldreich, and M. Luby. Towards a theory of average case complexity. In Proceedings 21th Annual ACM Symposium on Theory of Computing, Seatle, Washington, 1989.Google Scholar
  2. [2]
    A. Goldberg, P. Purdom, and C. Brown. Average time analysis of simplified davis-putnan procedures. Information Processing Letters, 15:72–75, 1982.Google Scholar
  3. [3]
    A. V. Goldberg and A. Marchetti-Spaccamela. On finding the exact solution of a zero-one knapsack problem. In Proceedings 16th Annual ACM Symposium on Theory of Computing, New York, 1984.Google Scholar
  4. [4]
    J. Hartmanis. On sparse sets in NP-P. Information Processing Letters, 16:55–60, 1983.Google Scholar
  5. [5]
    D. S. Johnson. The NP-completeness column: An ongoing guide. Journal of Algorithms, (5):284–299, 1984.Google Scholar
  6. [6]
    K. Ko and D. More. Completeness, approximation and density. SIAM Journal of Computing, 10:787–796, 1981.Google Scholar
  7. [7]
    J. C. Lagarias and A. M. Odlyzko. Solving low-density subset sum problems. In Proceedings 24th Annual Symposium on Foundations of Computer Science, Los Angeles, 1983.Google Scholar
  8. [8]
    L. A. Levin. Problems complete in average instance. In Proceedings 16th Annual ACM Symposium on Theory of Computing, 1984.Google Scholar
  9. [9]
    N. A. Lynch. Approximations to the halting problem. J. Comput. Syst. Science, 9:143–150, 1974.Google Scholar
  10. [10]
    C. H. Papadimitriou and M. Yannakakis. Optimization, approximation and complexity classes. In Proceedings 20th Annual ACM Symposium on Theory of Computing, pages 229–234, 1988.Google Scholar
  11. [11]
    A. Paz and S. Moran. Non deterministic polynomial optimization problems and their approximation. Theoretical Computer Science, 15:251–277, 1981.Google Scholar
  12. [12]
    J. Rolim. Towards a complexity theory for approximation languages. paper presented at the 3rd. Symposium on Complexity of Approximately Solved Problems at Columbia University, New York, April 1989.Google Scholar
  13. [13]
    J. Rolim and S. Greibach. On the IO-complexity and approximation languages. Information Processing Letters, 28(1):27–31, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • José D. P. Rolim
    • 1
  1. 1.Department of Mathematics and Computer ScienceOdense UniversityOdenseDenmark

Personalised recommendations