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We show that there is a deterministic local algorithm (constant-timedistributed graph algorithm) that finds a 5-approximation of a minimumdominating set on outerplanar graphs. We show there is no such algorithm thatfinds a $(5-\varepsilon)$-approximation, for any $\varepsilon>0$. Our algorithmonly requires knowledge of the degree of a vertex and of its neighbors, so thatlarge messages and unique identifiers are not needed.

A tight local algorithm for the minimum dominating set problem in outerplanar graphs