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
Battiti, R., Bertossi, A.A., Bonucceli, M.A.: Assigning code in wireless networks: bounds and scaling properties. Wireless Networks 5, 195–209 (1999)
Beauquier, J., Kumar Datta, A., Gradinariu, M., Magniette, F.: Self-Stabilizing Local Mutual Exclusion and Definition Refinement. Chicago Journal of Theoretical Computer Science (2002)
Chachis, G.C.: If it walks like a duck: nanosensor threat assessment. In: Proc. SPIE, vol. 5090, pp. 341–347 (2003)
Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Communications of the ACM 17, 643–644 (1974)
Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)
Ghosh, S., Karaata, M.H.: A Self-Stabilizing Algorithm for Coloring Planar Graphs. Distributed Computing 7, 55–59 (1993)
Grundy, P.M.: Mathematics and games. Eureka 2, 6–8 (1939)
Goddard, W., Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Fault Tolerant Algorithms for Orderings and Colorings. In: Proc. IPDP 2004 (2004)
Gradinariu, M., Tixeuil, S.: Self-stabilizing Vertex Coloring of Arbitrary Graphs. In: Proc. OPODIS 2000, pp. 55–70 (2000)
Hedetniemi, S.T., Jacobs, D.P., Srimani, P.K.: Linear time self-stabilizing colorings. Information Processing Letters 87, 251–255 (2003)
Hu, L.: Distributed code assignments for CDMA Packet Radio Network. IEEE/ACM Transactions on Networking 1, 668–677 (1993)
Huang, S.T., Hung, S.S., Tzeng, C.H.: Self-stabilizing coloration in anonymous planar networks. Information Processing Letters 95, 307–312 (2005)
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)
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)
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)
Sur, S., Srimani, P.K.: A self-stabilizing algorithm for coloring bipartite graphs. Information Sciences 69, 219–227 (1993)
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Kosowski, A., Kuszner, Ł. (2006). Self-stabilizing Algorithms for Graph Coloring with Improved Performance Guarantees. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2006. ICAISC 2006. Lecture Notes in Computer Science(), vol 4029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785231_120
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DOI: https://doi.org/10.1007/11785231_120
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