Fast Distributed Approximations in Planar Graphs

@inproceedings{Czygrinow2008FastDA,
  title={Fast Distributed Approximations in Planar Graphs},
  author={Andrzej Czygrinow and Michal Hanckowiak and Wojciech Wawrzyniak},
  booktitle={DISC},
  year={2008}
}
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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Hańćkowiak, Distributed algorithms for weighted problems in sparse graphs

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