  We consider whether it is possible to find ground states of frustrated spin
systems by solving them locally. Using spin glass physics and Imry-Ma arguments
in addition to numerical benchmarks we quantify the power of such local
solution methods and show that for the average low-dimensional spin glass
problem outside the spin- glass phase the exact ground state can be found in
polynomial time. In the second part we present a heuristic, general-purpose
hierarchical approach which for spin glasses on chimera graphs and lattices in
two and three dimensions outperforms, to our knowledge, any other solver
currently around, with significantly better scaling performance than simulated
annealing.
