Grammars for machine translation can be materialized on demand by finding source phrases in an indexed parallel corpus and extracting their translations. This approach is limited in practical applications by the computational expense of online lookup and extraction. For phrase-based models, recent work has shown that on-demand grammar extraction can be greatly accelerated by parallelization on general purpose graphics processing units (GPUs), but these algorithms do not work for hierarchical models, which require matching patterns that contain gaps. We address this limitation by presenting a novel GPU algorithm for on-demand hierarchical grammar extraction that is at least an order of magnitude faster than a comparable CPU algorithm when pr...