Brief announcement: local approximability of minimum dominating set on planar graphs

@article{Hilke2014BriefAL,
title={Brief announcement: local approximability of minimum dominating set on planar graphs},
author={Miikka Hilke and C. Lenzen and J. Suomela},
journal={ArXiv},
year={2014},
volume={abs/1402.2549}
}

We show that there is no deterministic local algorithm (constant-time distributed graph algorithm) that finds a (7-ε)-approximation of a minimum dominating set on planar graphs, for any positive constant ε. In prior work, the best lower bound on the approximation ratio has been 5-ε; there is also an upper bound of 52.