A Local 6-Approximation Distributed Algorithm for Minimum Dominating Set Problem in Planar Triangle-Free Graphs

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.