Faster algorithms for vertex partitioning problems parameterized by clique-width.

•Dominating set for graphs of clique-width k.•Naive approach will solve in time 4(2(3k))poly(n).•The previous best algorithm by Bui-Xuan et al.: 2(O(k2))poly(n) by using rank-width.•Ours: 2O(klogk)poly(n) by inventing a new trick using Q-rank-width.•This is the FIRST paper to use Q-rank-width for the faster dynamic-programming algorithm.