  Weighted independent domination is an NP-hard graph problem, which remains
computationally intractable in many restricted graph classes. In particular,
the problem is NP-hard in the classes of sat-graphs and chordal graphs. We
strengthen these results by showing that the problem is NP-hard in a proper
subclass of the intersection of sat-graphs and chordal graphs. On the other
hand, we identify two new classes of graphs where the problem admits
polynomial-time solutions.
