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Abstract

We use Martingale inequalities to give a simple and uniform analysis of two families of distributed randomised algorithms for edge colouring graphs.

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References

  1. 1.
    Bollabas, B.: Graph Theory: An Introductory Course. Springer, Heidelberg (1980)Google Scholar
  2. 2.
    Dubhashi, D., Grable, D.A., Panconesi, A.: Near optimal distributed edge colouring via the nibble method. Theoretical Computer Science 203, 225–251 (1998); A special issue for ESA 1995, the 3rd European Symposium on AlgorithmsGoogle Scholar
  3. 3.
    Dubhashi, D., Panconesi, A.: Concentration of measure for computer scientists. Draft of a monograph in preparationGoogle Scholar
  4. 4.
    Grable, D., Panconesi, A.: Near optimal distributed edge colouring in O(log log n) rounds. Random Structures and Algorithms 10(3), 385–405 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Grable, D., Panconesi, P.: Brooks and Vizing Colurings, SODA 98Google Scholar
  6. 6.
    Luby, M.: Removing randomness in parallel without a processor penalty. J. Computer and Systems Sciences 47(2), 250–286 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Marton, K.: Bounding \({\bar d}\) distance by informational divergence: A method to prove measure concentration. Annals of Probability 24, 857–866 (1996)Google Scholar
  8. 8.
    Marton, K.: On the measure concentration inequality of Talagrand for dependent random variables. Submitted for publication (1998) Google Scholar
  9. 9.
    McDiarmid, C.J.H.: On the method of bounded differences. In: Siemons, J. (ed.) Surveys in Combinatorics. London Mathematical Society Lecture Notes Series 141. Cambridge University Press, Cambridge (1989)Google Scholar
  10. 10.
    Molloy, M., Reed, B.: A bound on the strong chromatic index of a graph. J. Comb. Theory (B) 69, 103–109 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Panconesi, A., Srinivasan, A.: Randomized distributed edge coloring via an extension of the Chernoff–Hoeffding bounds. SIAM J. Computing 26(2), 350–368 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Spencer, J.: Probabilistic methods in combinatorics. In: Proceedings of the International Congress of Mathematicians, Zurich, Birkhauser (1995)Google Scholar
  13. 13.
    Talagrand, M.: Concentration of measure and isoperimetric inequalities in product spaces. Publ. math. IHES 81(2), 73–205 (1995)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Devdatt P. Dubhashi
    • 1
  1. 1.Department of Computer Science and EnggIndian Institute of Technology, DelhiNew DelhiIndia

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