A Tight Local Algorithm for the Minimum Dominating Set Problem in Outerplanar Graphs
Marthe Bonamy, Cook, Linda, Carla Groenland, Alexandra Wesolek · arXiv (Cornell University) · 2021
We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a $(5-\varepsilon)$-approximation, for any $\varepsilon>0$. Our algorithm only requires knowledge of the degree of a vertex and of its neighbors, so that large messages and unique identifiers are not needed.