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Statistical Mechanics in Optimization Problems

  • Pik-Yin Lai
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 45)

Abstract

The idea of treating certain difficult combinatorial optimization problems using the concepts and techniques in statistical mechanics is discussed. The NP-complete problem of graph coloring is used as a simple illustration.

Keywords

Statistical Mechanic Spin Glass Chromatic Number Graph Coloring Polynomial Algorithm 
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.

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References

  1. 1.
    Gaxey M.R. and Johnson D.S., in Computers and Intractability, ( San Francisco: Freeman 1979 )Google Scholar
  2. 2.
    Karp R.M., in Complexity of Computer Computations edited by R.E. Miller and J.W. Thather p.85 (Plenum Press 1972)Google Scholar
  3. 3.
    Vannimenus J. and Mezard M., J. Physique Lett., 45, L1145 (1984)CrossRefGoogle Scholar
  4. 4.
    Mezard M. and Parisi G., J. Physique, 47, 1285 (1986)CrossRefGoogle Scholar
  5. 5.
    Fu Y. and Anderson P. W., J. Phys. A, 19, 1605 (1986)CrossRefzbMATHADSMathSciNetGoogle Scholar
  6. 6.
    Lai P-Y and Goldschmidt Y. Y., J. Stat. Phys., 48, 513 (1987)CrossRefzbMATHADSMathSciNetGoogle Scholar
  7. 7.
    Goldschmidt Y. Y. and Lai P-Y, J. Phys. A, 21, L1043 (1988)CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Bouchaud J.P. and Le Doussal P., Europhys. Lett., 1, 91 (1986)CrossRefADSGoogle Scholar
  9. 9.
    Orland H., J. Physique Lett., 46, L763 (1985)CrossRefGoogle Scholar
  10. 10.
    Kirkpatrick S., Gelatt C. D. and Vecchi M. P. Jr., Science, 220, 671 (1983)CrossRefzbMATHADSMathSciNetGoogle Scholar
  11. 11.
    Appel K. and Haken W., Sci. Am., (Oct. 1977), Bull. Am. Math. Soc., 82, 711 (1976)Google Scholar
  12. 12.
    Erdos P. and Spencer J., in Probabilistic methods in combinatorics ( New York and London: Academic Press 1974 )Google Scholar
  13. 13.
    Bollobas B. and Erdos P., Math. Proc. Camb. Phil. Soc., 80, 419 (1976)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    McDiarmid C., Ann. Oper. Res., 1, 183 (1984)CrossRefGoogle Scholar
  15. 15.
    McDiarmid C., SIAM J. Comput., 8, 1 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Johri A. and Matula D.W.,in Technical Report 82-CSE-6, Southern Methodist University, Dallas TX (1982)Google Scholar
  17. 17.
    Wu F.Y., Rev. Mod. Phys., 54, 235 (1982)CrossRefADSGoogle Scholar
  18. 18.
    Baxter R., in Exactly solved models in statistical mechanics, p. 33 ( New York: Academic Press 1982 )zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Pik-Yin Lai
    • 1
  1. 1.Center for Simulational PhysicsUniversity of GeorgiaAthensUSA

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