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

Abstract

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 − ε)-approximation, for any ε > 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.