  We first devise a branching algorithm that computes a minimum independent
dominating set on any graph with running time O*(2^0.424n) and polynomial
space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A
branch-and-reduce algorithm for finding a minimum independent dominating set in
graphs, Proc. WG'06). We then show that, for every r>3, it is possible to
compute an r-((r-1)/r)log_2(r)-approximate solution for min independent
dominating set within time O*(2^(nlog_2(r)/r)).
