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Parallel and on-line graph coloring algorithms

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Algorithms and Computation (ISAAC 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 650))

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Abstract

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.

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References

  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. B. Berger and J. Rompel. A better performance guarantee for approximate graph coloring. Algorithmica, 5(4):459–466, 1990.

    Article  Google Scholar 

  3. R. Boppana and M. M. Halldórsson. Approximating maximum independent sets by excluding subgraphs. BIT, 32(2):180–196, June 1992.

    Google Scholar 

  4. P. ErdŐs and G. Szekeres. A combinatorial problem in geometry. Compositio Math., 2:463–470, 1935.

    Google Scholar 

  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. M. M. Halldórsson. A still better performance guarantee for approximate graph coloring. Technical Report 90-44, DIMACS, June 1990.

    Google Scholar 

  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. 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. 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. L. Lovász, M. Saks, and W. T. Trotter. An online graph coloring algorithm with sublinear performance ratio. Discrete Math., 75:319 325, 1989.

    Article  Google Scholar 

  11. M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput., 15:1036–1053, 1986.

    Article  Google Scholar 

  12. C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. Manuscript, July 1992.

    Google Scholar 

  13. S. Vishwanathan. Private communication.

    Google Scholar 

  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. A. Wigderson. Personal communications.

    Google Scholar 

  16. A. Wigderson. Improving the performance guarantee for approximate graph coloring. J. ACM, 30(4):729–735, 1983.

    Article  Google Scholar 

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Authors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Hokuriku Tatsunokuchi, 923-12, Ishikawa, Japan

    MagnÚs M. Halldórsson

Authors
  1. MagnÚs M. Halldórsson
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Editor information

Toshihide Ibaraki Yasuyoshi Inagaki Kazuo Iwama Takao Nishizeki Masafumi Yamashita

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© 1992 Springer-Verlag Berlin Heidelberg

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Halldórsson, M.M. (1992). Parallel and on-line graph coloring algorithms. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_58

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  • DOI: https://doi.org/10.1007/3-540-56279-6_58

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56279-5

  • Online ISBN: 978-3-540-47501-9

  • eBook Packages: Springer Book Archive

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