In this paper, we present a new distributed approximation algorithm for the minimum dominating set problem in planar triangle-free graphs. The algorithm operates in a constant number of rounds in the LOCAL model. Using the bunch technique, we prove that our algorithm achieves an approximation ratio of 6, which is a significant improvement over previous results for distributed algorithms, where the best known approximation ratio was 8 + ϵ for any ϵ > 0 . While sequential algorithms can achieve approximation ratios below 5 for this problem, our distributed algorithm achieves the best known approximation ratio in the LOCAL model. We provide a detailed proof and analysis of the algorithm, which can be implemented in a distributed manner. [ABSTRACT FROM AUTHOR]

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