We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth which are used to model wireless communication networks. The approach presented yields a robust algorithm, that is, it accepts any undirected graph as input, and returns a (1+ε)-approximate minimum independent dominating set, or a certificate showing that the input graph does not satisfy the bounded growth property.
Hurink, J. L., & Nieberg, T. (2008). Approximating minimum independent dominating sets in wireless networks. Information processing letters, 109(08332/2), 155-160. [10.1016/j.ipl.2008.09.021]. https://doi.org/10.1016/j.ipl.2008.09.021