Abstract
We present a self-stabilizing algorithm for the distance-2 coloring problem that uses a constant number of variables on each node and that stabilizes in O(Δ2 m) moves using at most Δ2 + 1 colors, where Δ is the maximum degree in the graph and m is the number of edges in the graph. The analysis holds true both for the sequential and the distributed adversarial daemon model. This should be compared with the previous best self-stabilizing algorithm for this problem which stabilizes in O(nm) moves under the sequential adversarial daemon and in O(n 3 m) time steps for the distributed adversarial daemon and which uses O(δ i ) variables on each node i, where δ i is the degree of node i.
Chapter PDF
References
Aardal, K.I., van Hoesel, S.P.M., Koster, A.M.C.A., Mannino, C., Sassano, A.: Models and solution techniques for frequency assignment problems. Ann. Op. Res. 153, 79–129 (2007)
Chaudhuri, P., Thompson, H.: A self-stabilizing distributed algorithm for edge-coloring general graphs. Aust. J. Comb. 38, 237–248 (2007)
Gairing, M., Goddard, W., Hedetniemi, S.T., Kristiansen, P., McRae, A.A.: Distance-two information in self-stabilizing algorithms. Par. Proc. L. 14, 387–398 (2004)
Ghosh, S., Karaata, M.H.: A self-stabilizing algorithm for coloring planar graphs. Dist. Comp. 7, 55–59 (1993)
Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Self-stabilizing algorithms for orderings and colorings. Int. J. Found. Comp. Sci. 16, 19–36 (2005)
Gradinariu, M., Johnen, C.: Self-stabilizing neighborhood unique naming under unfair scheduler. In: Sakellariou, R., Keane, J.A., Gurd, J.R., Freeman, L. (eds.) Euro-Par 2001. LNCS, vol. 2150, pp. 458–465. Springer, Heidelberg (2001)
Gradinariu, M., Tixeuil, S.: Self-stabilizing vertex coloring of arbitrary graphs. In: OPODIS 2000, pp. 55–70 (2000)
Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Linear time self-stabilizing coloring. Inf. Proc. Lett. 87, 251–255 (2003)
Huang, S.-T., Hung, S.-S., Tzeng, C.-H.: Self-stabilizing coloration in anonymous planar networks. Inf. Proc. Lett. 95, 307–312 (2005)
Kosowski, A., Kuszner, L.: Self-stabilizing algorithms for graph coloring with improved performance guarantees. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 1150–1159. Springer, Heidelberg (2006)
Shukla, S., Rosenkrantz, D., Ravi, S.: Developing self-stabilizing coloring algorithms via systematic randomization. In: Proc. Int. Workshop on Par. Process., pp. 668–673 (1994)
Shukla, S.K., Rosenkrantz, D., Ravi, S.S.: Observations on self-stabilizing graph algorithms for anonymous networks. In: Proc. of the Second Workshop on Self-stabilizing Systems, pp. 7.1–7.15 (1995)
Sun, H., Effantin, B., Kheddouci, H.: A self-stabilizing algorithm for the minimum color sum of a graph. In: Rao, S., Chatterjee, M., Jayanti, P., Murthy, C.S.R., Saha, S.K. (eds.) ICDCN 2008. LNCS, vol. 4904, pp. 209–214. Springer, Heidelberg (2008)
Sur, S., Srimani, P.K.: A self-stabilizing algorithm for coloring bipartite graphs. Inf. Sci. 69, 219–227 (1993)
Tzeng, C.-H., Jiang, J.-R., Huang, S.-T.: A self-stabilizing (δ + 4)-edge-coloring algorithm for planar graphs in anonymous uniform systems. Inf. Proc. Lett. 101, 168–173 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blair, J., Manne, F. (2010). An Efficient Self-stabilizing Distance-2 Coloring Algorithm. In: Kutten, S., Žerovnik, J. (eds) Structural Information and Communication Complexity. SIROCCO 2009. Lecture Notes in Computer Science, vol 5869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11476-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-11476-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11475-5
Online ISBN: 978-3-642-11476-2
eBook Packages: Computer ScienceComputer Science (R0)