Abstract
Let G = (V,E) be a simple undirected graph. A vertex colouring of G assigns colours to each vertex in such a way that neighbours have different colours.
In this paper we discuss how efficient (time and bits) vertex colouring may be accomplished by exchange of bits between neighbouring vertices. The distributed complexity of vertex colouring is of fundamental interest for the study and analysis of distributed computing. Usually, the topology of a distributed system is modelled by a graph and paradigms of distributed systems are encoded by classical problems in graph theory; among these classical problems one may cite the problems of vertex colouring, computing a maximal independent set, finding a vertex cover or finding a maximal matching. Each solution to one of these problems is a building block for many distributed algorithms: symmetry breaking, topology control, routing, resource allocation.
This work was supported by grant No ANR-06-SETI-015-03 awarded by Agence Nationale de la Recherche
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References
Bodlaender, H.L., Moran, S., Warmuth, M.K.: The distributed bit complexity of the ring: from the anonymous case to the non-anonymous case. Information and computation 114(2), 34–50 (1994)
Cole, R., Vishkin, U.: Deterministic coin tossing and accelerating cascades: micro and macro techniques for designing parallel algorithms. In: STOC, pp. 206–219 (1986)
Dinitz, Y., Moran, S., Rajsbaum, S.: Bit complexity of breaking and achieving symmetry in chains and rings. Journal of the ACM 55(1) (2008)
Finocchi, I., Panconesi, A., Silvestri, R.: An experimental analysis of simple, distributed vertex coloring algorithms. Algorithmica 41(1), 1–23 (2004)
Ghosh, S.: Distributed systems - An algorithmic approach. CRC Press, Boca Raton (2006)
Johansson, Ö.: Simple distributed (Δ + 1)-coloring of graphs. Information Processing Letters 70(5), 229–232 (1999)
Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press, Cambridge (1999)
Kothapalli, K., Onus, M., Scheideler, C., Schindelhauer, C.: Distributed coloring in \({O}(\sqrt{\log n})\) bit rounds. In: Proceedings of 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Rhodes Island, Greece, April 25-29. IEEE, Los Alamitos (2006)
Kuhn, F., Wattenhofer, R.: On the complexity of distributed graph coloring. In: Proceedings of the 25 Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 7–15. ACM Press, New York (2006)
Linial, N.: Locality in distributed graph algorithms. SIAM J. Comput. 21, 193–201 (1992)
Luby, M.: Removing randomness in parallel computation without a processor penalty. J. Comput. Syst. Sci. 47(2), 250–286 (1993)
Peleg, D.: Distributed computing - A Locality-sensitive approach. In: SIAM Monographs on discrete mathematics and applications (2000)
Santoro, N.: Design and analysis of distributed algorithms. Wiley, Chichester (2007)
Yao, A.C.: Some complexity questions related to distributed computing. In: Proceedings of the 11th ACM Symposium on Theory of computing (STOC), pp. 209–213. ACM Press, New York (1979)
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Métivier, Y., Robson, J.M., Saheb-Djahromi, N., Zemmari, A. (2009). Brief Annoucement: Analysis of an Optimal Bit Complexity Randomised Distributed Vertex Colouring Algorithm . In: Abdelzaher, T., Raynal, M., Santoro, N. (eds) Principles of Distributed Systems. OPODIS 2009. Lecture Notes in Computer Science, vol 5923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10877-8_28
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DOI: https://doi.org/10.1007/978-3-642-10877-8_28
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