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.

翻译：我们展示了一种确定性的本地算法( 固定时间分布式图表算法 ), 它在外平面图上找到一个5- 5 度的最小占位值。 我们显示没有这样的算法可以找到一个$( 5-\ varepsilon) $( $) 的( varepsilon) - adopolation $( $) 。 我们的算法只要求了解顶点及其邻居的程度, 因此不需要大的信息和独特的识别符 。