Coloring in sublinear time

  • Andreas Nolte
  • Rainer Schrader
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1284)


We will present an algorithm, based on SA-techniques and a sampling procedure, that colors a given random 3-colorable graph with high probability in sublinear time. This result is the first theoretical proof for the excellent experimental performance results of Simulated Annealing known from the literature when applied to graph coloring problems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alon, N.; Kahale, N.: A spectral technique for coloring random 3-colorable graphs, Proceedings of the 26th Symposium on Theory of Computing, 1994Google Scholar
  2. 2.
    Angluin, D.; Valiant, L.G.: Fast probabilistic algorithms for Hamiltonian circuits and matchings, Journal of Computer System Science 18, 1979Google Scholar
  3. 3.
    Blum, A.; Spencer, J.: Coloring Random and Semi-Random k-Colorable graphs, Journal of Algorithms 19, 1995Google Scholar
  4. 4.
    Chung, K.L.: Markov chains with stationary transition probabilities, Springer Verlag, Heidelberg, 1960.Google Scholar
  5. 5.
    Dyer, M.; Frieze, A.: The Solution of Some Random NP-Hard Problems in Polynomial Expected Time, Journal of Algorithms 10, 1989Google Scholar
  6. 6.
    Feller, W.: An introduction to probability theory and its applications, Volume 1, John Wiley & Sons, New York, 1950Google Scholar
  7. 7.
    Garey, M.R.; Johnson, S.J.: Computers and Intractability, W.H. Freeman and Company, 1979Google Scholar
  8. 8.
    Jensen, T.; Toft, B.: Graph Coloring Problems, John Wiley & Sons, 1995Google Scholar
  9. 9.
    Jerrum, J; Sorkin, G.: Simulated Annealing for Graph Bisection, Technical Report 1993, LFCS, University of EdinburghGoogle Scholar
  10. 10.
    Johnson, D.S.; Aragon, C.R.; McGeoch, L.A.; Schevon, C.: Optimization by Simulated Annealing: An Experimental Evaluation, Operations Research 39, 1991Google Scholar
  11. 11.
    Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P.: Optimization by Simulated Annealing, Science 220, 1983.Google Scholar
  12. 12.
    Kucera, L.: Expected behaviour of graph coloring algorithms, Lecture Notes in Computer Science 56, 1977Google Scholar
  13. 13.
    Laarhoven, P.J.M.; Aarts, E.H.L.: Simulated Annealing: Theory and Applications, Kluwer Academic Publishers, 1989.Google Scholar
  14. 14.
    Lindvall, T.: Lectures on the Coupling method, John Wiley & Sons, 1992Google Scholar
  15. 15.
    Metropolis, N.; Rosenbluth, M.; Rosenbluth, M.; Teller, A.; Teller, E.: Equation of state calculations by fast computer machines, Journal of Chemical Physics 21, 1953Google Scholar
  16. 16.
    Petford, A.D.; Welsh, D.J.A.: A Randomized 3-Coloring Algorithm, Discrete Mathematics 74 (1989), North HollandGoogle Scholar
  17. 17.
    Sasaki, G.H.; Hajek, B.: The Time Complexity of Maximum Matching by Simulated Annealing, Journal of the Association for Computing Machinery 35, 1988Google Scholar
  18. 18.
    Turner, J.: Almost All k-Colorable Graphs Are Easy to Color, Journal of Algorithms 9, 1988Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Andreas Nolte
    • 1
  • Rainer Schrader
    • 1
  1. 1.University of CologneCologneGermany

Personalised recommendations