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On Greedy Graph Coloring in the Distributed Model

  • Adrian Kosowski
  • Łukasz Kuszner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4128)

Abstract

In the paper we consider distributed algorithms for greedy graph coloring. For the largest-first (LF) approach, we propose a new distributed algorithm which is shown to color a graph in an expected time of O(ΔlognlogΔ) rounds, and we prove that any distributed LF-coloring algorithm requires at least Ω(Δ) rounds. We discuss the quality of obtained colorings in the general case and for particular graph classes. Finally, we show that other greedy graph coloring approaches, such as smallest-last (SL) or dynamic-saturation (SLF), are not suitable for application in distributed computing, requiring Ω(n) rounds.

Keywords

Graph Coloring Sequential Algorithm Graph Class Vertex Coloring Problem Uncolored Vertex 
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.
    Battiti, R., Bertossi, A.A., Bonuccelli, M.A.: Assigning codes in wireless networks. Wireless Networks 5, 195–209 (1999)CrossRefGoogle Scholar
  2. 2.
    Bellare, M., Goldreich, O., Sudan, M.: Free bits, PCPs and non-approximability — towards tight results. SIAM J. Comp. 27, 804–915 (1998)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Chaudhuri, P.: Algorithms for some graph problems on a distributed computational model. Information Sciences 43, 205–228 (1987)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Grable, D.A., Panconesi, A.: Fast distributed algorithms for Brooks-Vizing colorings. J. Algorithms 37, 85–120 (2000)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Grundy, P.M.: Mathematics and games. Eureka 2, 6–8 (1939)Google Scholar
  6. 6.
    Hansen, J., Kubale, M., Kuszner, Ł., Nadolski, A.: Distributed largest-first algorithm for graph coloring. In: Danelutto, M., Vanneschi, M., Laforenza, D. (eds.) Euro-Par 2004. LNCS, vol. 3149, pp. 804–811. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Johansson, Ö.: Simple distributed (Δ + 1)-coloring of graphs. Inf. Process. Lett. 70, 229–232 (1999)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kosowski, A., Manuszewski, M.: Classical Coloring of Graphs. In: Graph Colorings. AMS Contemporary Math., vol. 352, pp. 1–20. Providence, USA (2004)Google Scholar
  9. 9.
    Kubale, M.: Introduction to Computational Complexity and Algorithmic Graph Coloring. GTN, Gdańsk, Poland (1998)Google Scholar
  10. 10.
    Kubale, M., Kuszner, Ł.: A better practical algorithm for distributed graph coloring. In: Proc. PARELEC, pp. 72–75 (2002)Google Scholar
  11. 11.
    Linial, N.: Locality in distributed graph algorithms. SIAM J. Comput. 21, 193–201 (1992)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15, 1036–1053 (1986)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    De Marco, G., Pelc, A.: Fast distributed graph coloring with O(Δ) colors. In: Proc. SODA, pp. 630–635 (2001)Google Scholar
  14. 14.
    Olariu, S., Randall, J.: Welsh-Powell opposition graphs. Inf. Process. Lett. 31, 43–46 (1989)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Panconesi, A., Rizzi, R.: Some simple distributed algorithms for sparse networks. Distributed Computing 14, 97–100 (2001)CrossRefGoogle Scholar
  16. 16.
    Panconesi, A., Srinivasan, A.: Improved distributed algorithms for coloring and network decomposition problems. In: Proc. STOC, pp. 581–592 (1992)Google Scholar
  17. 17.
    Turner, J.S.: Almost all k-colorable graphs are easy to color. J. Algorithms 9, 63–82 (1988)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Adrian Kosowski
    • 1
  • Łukasz Kuszner
    • 1
  1. 1.Department of Algorithms and System ModelingGdańsk University of TechnologyPoland

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