  Dense, discrete Graphical Models with pairwise potentials are a powerful
class of models which are employed in state-of-the-art computer vision and
bio-imaging applications. This work introduces a new MAP-solver, based on the
popular Dual Block-Coordinate Ascent principle. Surprisingly, by making a small
change to the low-performing solver, the Max Product Linear Programming (MPLP)
algorithm, we derive the new solver MPLP++ that significantly outperforms all
existing solvers by a large margin, including the state-of-the-art solver
Tree-Reweighted Sequential (TRWS) message-passing algorithm. Additionally, our
solver is highly parallel, in contrast to TRWS, which gives a further boost in
performance with the proposed GPU and multi-thread CPU implementations. We
verify the superiority of our algorithm on dense problems from publicly
available benchmarks, as well, as a new benchmark for 6D Object Pose
estimation. We also provide an ablation study with respect to graph density.
