  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.
