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Self-stabilizing Algorithms for Graph Coloring with Improved Performance Guarantees

  • Adrian Kosowski
  • Łukasz Kuszner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)

Abstract

In the self-stabilizing model we consider a connected system of autonomous asynchronous nodes, each of which has only local information about the system. Regardless of the initial state, the system must achieve a desirable global state by executing a set of rules assigned to each node. The paper deals with the construction of a solution to graph coloring in this model, a problem motivated by code assignment in wireless networks.

A new method based on spanning trees is applied to give the first (to our knowledge) self-stabilizing algorithms working in a polynomial number of moves, which color bipartite graphs with exactly two colors. The complexity and performance characteristics of the presented algorithms are discussed for different graph classes.

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References

  1. 1.
    Battiti, R., Bertossi, A.A., Bonucceli, M.A.: Assigning code in wireless networks: bounds and scaling properties. Wireless Networks 5, 195–209 (1999)CrossRefGoogle Scholar
  2. 2.
    Beauquier, J., Kumar Datta, A., Gradinariu, M., Magniette, F.: Self-Stabilizing Local Mutual Exclusion and Definition Refinement. Chicago Journal of Theoretical Computer Science (2002)Google Scholar
  3. 3.
    Chachis, G.C.: If it walks like a duck: nanosensor threat assessment. In: Proc. SPIE, vol. 5090, pp. 341–347 (2003)Google Scholar
  4. 4.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17, 643–644 (1974)zbMATHCrossRefGoogle Scholar
  5. 5.
    Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  6. 6.
    Ghosh, S., Karaata, M.H.: A Self-Stabilizing Algorithm for Coloring Planar Graphs. Distributed Computing 7, 55–59 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Grundy, P.M.: Mathematics and games. Eureka 2, 6–8 (1939)Google Scholar
  8. 8.
    Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Fault Tolerant Algorithms for Orderings and Colorings. In: Proc.  IPDP 2004 (2004)Google Scholar
  9. 9.
    Gradinariu, M., Tixeuil, S.: Self-stabilizing Vertex Coloring of Arbitrary Graphs. In: Proc. OPODIS 2000, pp. 55–70 (2000)Google Scholar
  10. 10.
    Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Linear time self-stabilizing colorings. Information Processing Letters 87, 251–255 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hu, L.: Distributed code assignments for CDMA Packet Radio Network. IEEE/ACM Transactions on Networking 1, 668–677 (1993)CrossRefGoogle Scholar
  12. 12.
    Huang, S.T., Hung, S.S., Tzeng, C.H.: Self-stabilizing coloration in anonymous planar networks. Information Processing Letters 95, 307–312 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hung, K.W., Yum, T.S.: An efficient code assignment algorithm for multihop spread spectrum packet radio networks. In: Proc. GLOBECOM 1990, pp. 271–274 (1990)Google Scholar
  14. 14.
    Kosowski, A., Kuszner, Ł: A self-stabilizing algorithm for finding a spanning tree in a polynomial number of moves. In: Wyrzykowski, R., Dongarra, J., Meyer, N., Waśniewski, J. (eds.) PPAM 2005. LNCS, vol. 3911, Springer, Heidelberg (2006)Google Scholar
  15. 15.
    Li, J., Blake, C., De Couto, D.S., Lee, H.I., Morris, R.: Capacity of Ad Hoc wireless networks. In: Proc. MobiCom 2001, pp. 61–69. ACM Press, New York (2001)Google Scholar
  16. 16.
    Sur, S., Srimani, P.K.: A self-stabilizing algorithm for coloring bipartite graphs. Information Sciences 69, 219–227 (1993)zbMATHCrossRefMathSciNetGoogle 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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