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An Incremental Distributed Algorithm for a Partial Grundy Coloring of Graphs

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Parallel and Distributed Processing and Applications (ISPA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4742))

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Abstract

A coloring of a graph G = (V,E) is a partition of {V 1,V 2 ⋯ V k } of V into k independent sets called color classes. A vertex v ∈ V i is called a Grundy vertex if it is adjacent to at least one vertex in color class V j , for every j < i. In the partial Grundy coloring, every color class contains at least one Grundy vertex. Such a coloring gives a partitioning of the graph into clusters for which every cluster has a clusterhead (the Grundy vertex) adjacent to some other clusters. Such a decomposition is very interesting for large distributed systems and networks. In this paper, we propose a distributed algorithm to maintain the partial Grundy coloring of any graph G when an edge is added

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References

  1. Antonoiu, G., Srimani, P.K.: A self-stabilizing distributed algorithm for minimal spanning tree problem in a symmetric graph. Computer & Mathematics with Application 35(10), 15–23 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bui, M., Butelle, F., Lavault, C.: A distributed algorithm for constructing a minimum diameter spanning tree. Journal of Parallel and Distributed Computing 64, 571–577 (2004)

    Article  MATH  Google Scholar 

  3. Christen, C.A., Selkow, S.M.: Some perfect coloring properties of graphs. Journal of Combinatorial Theory B27, 49–59 (1979)

    Article  MathSciNet  Google Scholar 

  4. Cockayne, E.J., Thommason, A.G.: Ordered Colourings of graphs. Journal of Combinatorial Theory B32, 286–292 (1982)

    Article  Google Scholar 

  5. Effantin, B., Kheddouci, H.: Grundy number of graphs. Discussiones Mathematicae Graph Theory 27(1), 5–18 (2007)

    MATH  MathSciNet  Google Scholar 

  6. Effantin, B., Kheddouci, H.: A Distributed Algorithm for a b-Coloring of a Graph. In: Guo, M., Yang, L.T., Di Martino, B., Zima, H.P., Dongarra, J., Tang, F. (eds.) ISPA 2006. LNCS, vol. 4330, pp. 430–438. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Erdös, P., Hare, W.R., Hedetniemi, S.T., Laskar, R.: On the equality of the Grundy and ochromatic numbers of a graph. Journal of Graph Theory 11(2), 157–159 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  8. Erdös, P., Hedetniemi, S.T., Laskar, R.C., Prins, G.C.E.: On the equality of the partial Grundy and upper ochromatic numbers of graphs. Discrete Mathematics 272, 53–64 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fujie, T.: An exact algorithm for the maximum leaf spanning tree problem. Computers & Operations Research 30, 1931–1944 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Germain, C., Kheddouci, H.: Grundy numbers of powers of graphs. Discrete Mathematics (to appear)

    Google Scholar 

  11. Hedetniemi, S.M., Hedetniemi, S.T., Beyer, T.: A linear algorithm for the Grundy (coloring) number of a tree. Congressus Numerantium 36, 351–363 (1982)

    MathSciNet  Google Scholar 

  12. Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Linear time self-stabilizing colorings. Information Processing Letters 87, 251–255 (2003)

    Article  MathSciNet  Google Scholar 

  13. Huang, S.-T., Hung, S.-S., Tzeng, C.-H.: Self-stabilizing coloration in anonymous planar networks. Information Processing Letters 95, 307–312 (2005)

    Article  MathSciNet  Google Scholar 

  14. Shi, Z., Goddard, W., Hedetniemi, S.T., Kennedy, K., Laskar, R., MacRae, A.: An algorithm for partial Grundy number on trees. Discrete Mathematics 304, 108–116 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Shi, Z., Goddard, W., Hedetniemi, S.T.: An anonymous self-stabilizing algorithm for 1-maximal independent set in trees. Information Processing Letters 91, 77–83 (2004)

    Article  MathSciNet  Google Scholar 

  16. Šparl, P., Žerovnik, J.: 2-local distributed algorithms for generalized coloring of hexagonal graphs. Electronic notes in Discrete Mathematics 22, 321–325 (2005)

    Article  Google Scholar 

  17. Telle, J.A., Proskurowski, A.: Algorithms for vertex partitioning problems on partial k-trees. SIAM Journal on Discrete Mathematics 10(4), 529–550 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Université de Lyon, Lyon, F-69003, France , Laboratoire LIESP, Université Lyon1, IUTA, Département Informatique, 71 rue Peter Fink, F-01000 Bourg en Bresse, France

    Lyes Dekar

  2. Université de Lyon, Lyon, F-69003, France , Laboratoire LIESP, Université Lyon1, Bâtiment Nautibus (ex.710), 43 bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

    Brice Effantin & Hamamache Kheddouci

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  1. Lyes Dekar
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  2. Brice Effantin
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  3. Hamamache Kheddouci
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Ivan Stojmenovic Ruppa K. Thulasiram Laurence T. Yang Weijia Jia Minyi Guo Rodrigo Fernandes de Mello

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© 2007 Springer-Verlag Berlin Heidelberg

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Dekar, L., Effantin, B., Kheddouci, H. (2007). An Incremental Distributed Algorithm for a Partial Grundy Coloring of Graphs. In: Stojmenovic, I., Thulasiram, R.K., Yang, L.T., Jia, W., Guo, M., de Mello, R.F. (eds) Parallel and Distributed Processing and Applications. ISPA 2007. Lecture Notes in Computer Science, vol 4742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74742-0_18

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  • DOI: https://doi.org/10.1007/978-3-540-74742-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74741-3

  • Online ISBN: 978-3-540-74742-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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