Parallel and on-line graph coloring algorithms

  • MagnÚs M. Halldórsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)


We discover a surprising connection between graph coloring algorithms in two orthogonal paradigms: parallel and on-line computing. We present a randomized on-line coloring algorithm with a performance guarantee of O(n/log n), an improvement of √log n factor. Also, from the same principle, we construct a parallel coloring algorithm with the same performance guarantee, for the first such result. Finally, we show how to apply the parallel algorithm to obtain an \(\mathcal{N}\mathcal{C}\) approximation algorithm for the independent set problem.


Chromatic Number Performance Guarantee Color Class Coloring Algorithm Pivot Node 
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  1. 1.
    S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and intractability of approximation problems. Manuscript, Apr. 1992.Google Scholar
  2. 2.
    B. Berger and J. Rompel. A better performance guarantee for approximate graph coloring. Algorithmica, 5(4):459–466, 1990.CrossRefGoogle Scholar
  3. 3.
    R. Boppana and M. M. Halldórsson. Approximating maximum independent sets by excluding subgraphs. BIT, 32(2):180–196, June 1992.Google Scholar
  4. 4.
    P. ErdŐs and G. Szekeres. A combinatorial problem in geometry. Compositio Math., 2:463–470, 1935.Google Scholar
  5. 5.
    M. Goldberg and T. Spencer. Constructing a maximal independent set in parallel. SIAM J. Comput., 2(3):322–328, Aug. 1989.Google Scholar
  6. 6.
    M. M. Halldórsson. A still better performance guarantee for approximate graph coloring. Technical Report 90-44, DIMACS, June 1990.Google Scholar
  7. 7.
    M. M. Halldórsson and M. Szegedy. Lower bounds for on-line graph coloring. In Proc. of the Third ACM-SIAM Symp. on Discrete Algorithms, pages 211–216, Jan. 1992.Google Scholar
  8. 8.
    D. S. Johnson. Worst case behaviour of graph coloring algorithms. In Proc. 5th Southeastern Conf. on Combinatorics, Graph Theory, and Computing. Congressus Numerantium X, pages 513–527, 1974.Google Scholar
  9. 9.
    R. Karp and V. Ramachandran. A survey of parallel algorithms for shared-memory machines. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume A. Elsevier Science Publishers B.V., 1990.Google Scholar
  10. 10.
    L. Lovász, M. Saks, and W. T. Trotter. An online graph coloring algorithm with sublinear performance ratio. Discrete Math., 75:319 325, 1989.CrossRefGoogle Scholar
  11. 11.
    M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput., 15:1036–1053, 1986.CrossRefGoogle Scholar
  12. 12.
    C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. Manuscript, July 1992.Google Scholar
  13. 13.
    S. Vishwanathan. Private communication.Google Scholar
  14. 14.
    S. Vishwanathan. Randomized online graph coloring. In Proc. 31st Ann. IEEE Symp. on Found. of Comp. Sci., pages 464–469, Oct. 1990.Google Scholar
  15. 15.
    A. Wigderson. Personal communications.Google Scholar
  16. 16.
    A. Wigderson. Improving the performance guarantee for approximate graph coloring. J. ACM, 30(4):729–735, 1983.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • MagnÚs M. Halldórsson
    • 1
  1. 1.Japan Advanced Institute of Science and TechnologyIshikawaJapan

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