Abstract
We give deterministic distributed algorithms that given δ> 0 find in a planar graph G, (1±δ)-approximations of a maximum independent set, a maximum matching, and a minimum dominating set. The algorithms run in O(log*|G|) rounds. In addition, we prove that no faster deterministic approximation is possible and show that if randomization is allowed it is possible to beat the lower bound for deterministic algorithms.
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Czygrinow, A., Hańćkowiak, M., Wawrzyniak, W. (2008). Fast Distributed Approximations in Planar Graphs. In: Taubenfeld, G. (eds) Distributed Computing. DISC 2008. Lecture Notes in Computer Science, vol 5218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87779-0_6
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DOI: https://doi.org/10.1007/978-3-540-87779-0_6
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